Richard J. Büchi (1924-1984)

H a n d s c h r i f t e n und Autographen d e r ETH-Bibliothek

64

Richard J. Büchi

Zürich: Wissenschaftshistorische Samnlungen d e r ETH-Bibliothek

1986

B ü C h i, Richard

J.

(1924-1984) Mathematiker

Hs 1175:l

ff.:

B i l d u n g s g a n g , B i o g r a p h i s c h e s

...

Zeugnisse

Primar- und Realschule der Stadt St.Gallen, 1930-34 2 Brosch.

St.gallische Kantonsschule, untere/obere technische Abteilung

& obere Klassen der Oberrealschule, 1939-43.

5

B1.

Maturitätszeugnis, st.gallische Kantonsschule.

1943.

1 B1.

ETHZürich:Einschreibeheft für Studierende, Abt.f.Mathernatik und Physik, WS 1943-WS

1946/7.

Brosch.

Bestätigungen der Vor- und Schlussdiplomprüfung und der Diplomerteilung(Kopien) an der ETH Zürich.

3

B1.

Verschiedene Ausweise (Religionsunterricht, Konfirmation, turnerischer Vorunterricht usw.). 9 B1.

Mittelschulhefte

Ordner nMittelschulstoff : Umschlag

Formeln, 9 B1.

Geometrie (Stereometrie); 65 B1.

Algebra

Zinseszins- & Rentenrechnung. B1.A 1

-

¹¹

Kombinatorik. B1.12-30 Komplexe Zahlen. 18 B1.

Funktionenlehre oder Analysis. 25 B1.

Physik

Kalorik. 32 B1.

Elektrizität. 25 B1.

Chemie

Matura 1941. 2 B1.

Kohlenstoff.

7

B1.

Stickstoff. B1.a-U Halogene.

14

B1.

Organische Chemie. B1.a-r

Verschiedene Mittelschulhefte:

Naturgeschichte lb. 2 Hefte & 4 lose B1.

Zoologie; Allgemeine Botanik 1 t. 1 Heft

Unser Körper; naturkundliches Skizzenheft I1 t. Brosch.m.erg.

B1.

Kartenlehre 111 b. 2 Hefte Kryptogamen; 3 t. 1 Heft

Physik-Textheft.

1

Steifbrosch.

W.Kopp. Lehrmittel des Physikunterrichtes der Kantonsschule St.Gallen (~ptik). II.Auf1.1937. 27 vervielf.& handschr.erg.S.

Chemie. Presspanheft Mineralogie. do.

Klausuren u.a. 5 B1.

Handschriftliche Aufzeichnun~en der ETH-Vorlesungen 38 F.Bäbler. Variationsrechnung.

WS

1944/5. 30 B1.

Beno Eckmann. Grundlagen der Analysis. WS 1944/5.

64

B1.

id. Topologie. WS 1945/6.

74

B1.

Heinz Hopf. Topologische Räume. SS 1945. 53 B1.

id. Ausgewählte Kapitel aus der linearen Algebra. WS 1945/6 53 Bi.

id. Algebraische Topologie. SS

1946. 49

B1.

Ed. Stief el. Kontinuierliche Gruppen. WS 1945/6, Ss

1946.

65 BI.

Paul Bernays. Mengenlehre. WS 1945/6.

49

B1.

Beweis

für

die Möglichkeit der Division im Bereich der Wohl- ordnungstypen. Abkürzungen & Bezeichnungen.

4~1. /s.

^Typoskr.

id. Grundlagen der Mathematik.

SS

1946? 8 B1.

id. Mathematische Logik.

WS 1946/7.

18 B1.

Alb. Pfluger. Integralgleichungen. WS l947/8.

44

BI.

49.

Gregor Wentzel. Elektrodynamik. SS 1945. 58 B1.

50. id. Uebungen. SS 1945.

14

B1.

51.

id. Zusammenfassung. 25 Blättchen 52. Formeln.

6

Blättchen

53. id. Optik. WS 1945/6 72 BI.

54.

id. Optik-Uebungen. WS 1945/6. 10 BI.

55. Zusammenfassung. 15 B1.

55a. Inhalt, 2 Blättchen 56. Formeln,

14

Blättchen

57.

id. Molekular-Statistik.

SS 1946.

32 B1.

58

.

Kinetische Theorie der Gase. Zusammenfassung nach Wentzel.

23

B1.

59. id. Elektronentheorie. WS

1946/7.

22 B1.

60.

id. Quantenstatistik. WS

1946/7. 38

B1.

61.

Wolfgang Pauli. Thermodynamik. SS

1946. 31

B1.

62. id. Uebungen.

16

BI.

63, id. Wellenmechanik. SS

1946.

11 BI.

64.

id. Statistische Mechanik. WS 1946/7. 38 B1.

+

(einschliesslich) Quantenstatistik, B1.39-61.

65. id. Uebungen hierzu.

14

B1.

66.

Seminar Lineare Algebra (quantitative

ragen),

m.Seminarvortrag von Büchi, o.J. 5

+

^{5 B1.}

+

lose Notizen.

1

Dossier

67.

Plancherel & Pfluger: Seminar über Approximationsmethoden. WS

1945/6. 32

B1.

68.

Henryk Schärf. Funktionen in topologischen Räumen. WS

1945/6.

Ca.40 B1.

69.

Problem von Wiener im L-Raum, 0.J. 10 B1.

+

lose Notizen. 1 Dossier

70*1

Konvergenzräume ;

15

B1.

.2 Topologische Räume;

7

B1.

.3

Konvergenz im topologischen Raum;

7

B1.

Dossier Gewebe

Stiefel, Seminar: Geometrie der Gewebe. WS

1946/7.

18 B1.

Aufgaben.

23

B1.

Vortrag: Gewebe und Grundlagen der affinen Geometrie; ca.30 B1.

Büchi: Webs and Groups. Geom.Sern.(~niv.of Michigan)

1953.

12 BI.

+

lose Notizen 1 Dossier

Mäppchen I1

Eine Klasse von R.A. (relational ~ l ~ e b r a ) : 0.J.

16

B1.

G.

Y.

Rainich: Ternary Relations in ~eometri and Algebra. SA p.

97-

112,

1952

(Michigan); beiliegend: Büchi, Formalised langugages for generalised equational relations, 2 B1.

Büchi, Eine abstrakte Theorie der Orientierung; 0.J. 2 B1.

Versch.Notizen. 1 Dossier

Mäppchen I11 (Probleme & Ideen, 0.J.; darunter:) sei ein System von Symbolen..

."; ⁷

^B1.

"L sei eine vollständige Lattice mit den Eigenschaften..."; o.J.

4

B1.

Lattices mit Booletscher Vereinigung.

4

B1.

Einbettung in pseduocomplem. lattices.

5 BI.

Kann jede vollständige Boolelsche Algebra als Algebra der vollen Mengen eines Topologischen Raumes dargestellt werden?

3

B1.

Ein stärkerer Ideal-Begriff. 2 B1.

Lose Notizzettel, ca.40 B1. 1 Dossier

Unbeschriftetes Mäppchen m.div.(~deen-)Notizen:

Galois-Dossier, ca.30 unnum.Bl. 1 Dossier

Varia (-~otizen) 11

University of Chicago (Spring/~ummer

1949)

Antoni Zygmund: Advanced Theory of Functions. Chicago, Spring

'49.

31B1.

Saunders Mac Lane. Theory of fields. Chicago Summer

'49.

11 B1.

Marshall Harvey Stone. Boolean Algebra. Chicago Som.l49. 3 ^B1.

Knopp

Konrad Knopp. Theorie und Anwendung der unendlichen Reihen.

Exzerpt (vermutlich aus Ed.4,1947). 45 B1.

Notizheftchen (von vorn nach hinten & V.V. sowie vor- und rückseits meist mit versch.Stoff beschriebenes Heftchen mit ca.

50

B1. ) :

-

Infinitiesimalrechnung 1.Variabeln

-

^Mechanik

-

Differentialgleichungen

93.

Kl.Notizordner, 0.J.

.1

Funktionentheorie. 35

S.

.2 Partielle Differentialgleichungen 1.0rdnung. 22

S.

.3

Verschiedenes. 25 B1.

.4

Topologie. 10 B1.

.5 Physik (lag lose bei).

11

S.

.6 [Mathematische u.a.Varia, los beiliegend, ohne Titel; darin u.a.:]

-

Funktionen mehrerer Varablen

-

Vektorprodukte

USW.

National Science Foundation Washington

94

KSF-Proposals 1962-67 , 1959

95-101 Propo sals

1969-1977

102 Entwürfe für Propo sal s

103-106

NSF-Budgets

1966-68

bis 1973-1977 National Institute of Health

107

NIH

Proposal (rn.Vorläuf ern)

,

¹⁹⁶⁶

NB:

VERTRAULICH!

1 Dossier

7

Dossiers 1 Dossier

4

Dossiers 1 Dossier Nachlassgliederung

108 Papers, Notes, Books, &C. in order as found. Verzeichnis (von

~rof. ~iefkes)

.

45 xerokopierte

S.

3.09

Ordnung nach Sachgebieten. Xerokopie der Gliederung von Prof.

Siefkes, Bl.A,AA, C,D,G,L,?4T,Q,R,S,W,V.

110 Things to be published

-

Decisions concerning publications

-

Automata Theory Book.

4

B1.Xerokopie (von~rof ,~iefkes),

+ 3

B1.

Biographische Varia

111 Lebensläufe, Bibliographie (einschl .Doktoranden) 1 Dossier

112 Verstreutes zur Biographie do

.

Nachtrag März

1986

Biographische Varia

113-114

Biographische Reminiszenzen seines Bruders, Edgar Büchi. 2 B1.

115

Description of scientific activities. 1 Dossier

116-118

Literaturkartei

A-Z, +

^{Karten "vorm} Alphabettt

3

Dossiers Fussfassen in USA

119

Undatiertes: Lebensläufe u.a.

1

kl.Dossier 120-128

USA 1947-8

(~.a,126-8,Korr,~48 Schulpr.Rohn)

129-155

USA

1949, meist Korrespondenzen, darunter mit

-

Schulpräs.Pallmann:

135-6,138,140,147,149,151

-

Schulratssekr.Dr.Bosshardt: 142,144

-

Dr.Neukomrn,

ETH:

145

-

Prof.Alb.Perrier, Lausanne (Rotary Club

CH):

141,144,148,150

Fussfassen in USA, Forts.

156-175 USA 1950-2, meist Korrespondenzen, darunter mit

- Schulratspräs, Pallmann: l58,163-4,169 (=1950)

;

173-4 (=1952)

- Dr.G.Neukomrn, ETH: 160 (=1950)

- Dr.Bosshardt, ETH: 165 (=1950)

- Dir.A.Ernst, Luzern (Rotary Club CH): 161-2, 168 (=1950) 176-199 USA 1955: meist Korrespondenzen (u.a. mit Prof,H.R.Brahana,

Head of the Department of Mathematics, Univ.of Illinois, ~rbana) Universitätsunterricht

200 Course Descriptions, 1953-1984 1 Dossier 201 Präsenz-

&

Notenlisten der Studenten, handschr.

1

Dossier 202 Class Lists

(Computer-Ausdrücke),1966-

1 Dossier 203-215 Sabbaticals

&

Verwandtes, 1958-1984

216 Reiseformalitäten (1962,

&?)

1 kl.Dossier

B

ü C

h i, Richard J.

Hs 1176: 1 ff.

M a n

U

s k r i p t e undverwandtes

...

Korrespondenz

Craig-Tarski-Vaught-Büchi

bzgl.Abstraction 1955-1957, gel.m.Notizen

An application of Craigts Lemma to decidability of 1.order theories.

2

B1.

Note on equivalence of axiom-systems. 4 B1.

Three Uses of Herbrandts Theorem in Relating Model-theory and Proof-theory.

11

B1. + Anhang B1.12-18 ad

- ^{Robinsont s theorem}

- Padoas Method

Büchi-Craig, Notes on the Family PCAof Sets of Models. 6 B1.

Utilize Henkints method for prooving Löwenheim-Skolem-Gödel to get an analogy to Gentzents Hauptsatz. 9 B1.

Abstraction, a relationship defined between formal systems, by the use of models.

18

B1.

Strong form of the Definability-Theorems; To Craigts problem on p.23. 6 B1.

Analysation of AC

('9 into a hierarchy (u.a.?).8 B1.

... a reformulation of these results... S.3-4 Notations.

2

B1.

By supposition and Gödel's completness theorem. 3 B1.

Let ~[&,p] be... 4 B1.

Tarski, remarks on PC (pseudo-arith.

)

.

⁸

^B1.

Ackermannts Problem. 3 B1.

Example of

a

K~E/A<. . .

⁸

^B1.

The Boolean algebra AC (u.a.?).

7 B1.

Let P=... be a 1.order system of axioms... 3 B1.

Verschiedene meist 1-bl.Notizen. 1 Dossier

CA 1,

p.407, "Aggregates"

31 Klein-groups of algebraic aggregates. 62 B1.

32 Some remarks on Klein-groups and the necessity for formal methods. Colloquium lecture (I.sem.1953/54); ca.18 B1.

33 On not algebraic invariants which can be replaced by algebraic invariants. 7 BI.

34 A fundamental problem.4 B1.

35 A

=

(1, - - , ^n>

=

set of n elements...

8

kl.Halbkartonb1.

36 Verdnzelte Notizen

1

Dossier

N B . : Die S e i t e n z a h l e n nach den A b s c h n i t t - S i g e l n I z . 6 . A 1, p.28; D 2-3, p.23; ucw.) beziehen s i c h a u f P r o f . S i e f k e s l V e r z e i c h n i s " P a p e r s , Notec, Books & C . i n o r d e r a s found", Hs 1175 : 1081

37

q-theory. 22 B1.

38 Definition of

(3

^{from k}

39

Example of a cancellation-semi-group which has no anti- automorphism. 4 B1.

40

Anti-Automorphisms of a group and the Erlanger Program.

15 Bl., m.Beilage: The Erlangen Program, SA aus Math.Intel1.

Aug.1977 pp.22-30

Inner Product Structures.

9

B1.

Algebras of Relations

-

Quantifiers

-

Algebras of predicate- predicates.

llIRB ~etters"(??). Dossier m.meist einz.Notizbl., darunter Extension of

Z8

by its multiplicative a ~ t o m ~ g r o u p ; 6 B1,

1 Dossier An abstraction of the theory of two relations.

23

B1.

Boolelsche R.11,E.R. 9 B1.

Abstractions of field-theory.

6

B1.

Partial pseudo equivalence relations. 8 B1.

Abstractions of Field-theory.

Verschiedene Notizen, z.T.gebünde1-t. 1 Dossier Abstractions of Grouptheory

Dossier Wr.Grahamn. Versch.einz.Notizen 1 Dossier Boolean Groups. 7 B1.

Some Abstractions of Group theory. 2 B1.

A theory, of which Boolean Group is an abstraction. 4 B1.

E?quational axiomatization of poly-adic groups. 2 B1.

Polyadic-groups of Postls. 18 B1.

~xtension-of an abelian group

N

by Z 2

-

The Quaternian group.

9

B1.

Verschiedene einzelne Notizen; darunter

1

Dossier Ableitungen aus: J.Certaine, R.Baer, O.Taussky, LMenger.

11 B1.

58

Galois Theory of Elementary Axiomsystem [vormals: Relatively Categorical and Normal Theories]. Typoskript m.Handkorr.

18 Bl.m.Einschüben

59

Euclidian versus Affine Geometry [from A 2, p.251.

1

Dossier Meist ungebündelte Notizen

60

Axiomatic of Geometry in Terms of Involutions. Geometry Seminar, Michigan Aug.1955

[A

21.

31

BI.

61 (~ourse?-) Notes on group theory with emphasis on finite syrnmetric groups. Ca. 100 z.T.gebündelte A-5-B1. 1 Dossier

[AA 1,

p.371, Categories and Automata

62

Envelope ttCategories & Automatan with notes and manuscirpt

"Automata in general algebrasn by Samuel Eilenberg Jesse B.

Wright. 8 B1.

+ ⁵³

vervielf.HL

63

Büchi, Mathematische Theorie des Verhaltens endlicher Auto- maten. Typoskriptkopie von

[B

101 m.handschr.Korrekturen.

[AA

1-2, p.31/32], Automata, Algebras and regular Systems. Old notes GAMM. Bonn, Mai

1962. 4

einleit.Bl.

Kolloquium, Bonn 2.Feb.

1962.

24 B1.

Theory of algebraic systems. Malc.Sb.

35(77)1954

pp.

3-20.

9

Bl.hs.Notizen.

Math.Theorie der Automaten. Mainz

1961-2

Was in dieser Vorlesung nicht behandelt werden soll..

-

Complementäre und mehr präzise Bemerkungen zum Inhalt der Vorlesungen. 5 B1.

Vorbemerkung über algebraische Systeme. 18 B1.

Transitions-Algebra. 12 Bl.

Struktur und Verhalten eines Automaten. Bl.Ml-M20 Minimaltheorie. Zusammenfassung. 5 B1.

Verhaltens-Algorithmen für endliche Automaten. 8 B1.

Kleinere, z.T.gebündelte Notizen.

1

Dossier Notes for a paper on Algebraic Theory of feedback in discrete

systems. LAA 11

Algebraic foundation of Automata-Theory

-

Unary Algebra, a foundation for the theory of feedback in deserent systems.

1

+

^{8 B1.}

Unary algebras as deterministic digital devices. 10 BI.

Graphiken.

3

B1.

Mathematical theory of Automata

[M 11

Kurs von J.R.Büchi und J.B.Wright a.d.Univ.of Michigan, "Com- munication Sciences

403"

1960. Vervielfältigungen & Notizen.

1 Dossier

[AA

2, p.291, Regular Systems

Bibliogr.11,

17

78

Reguläre Kanonische Systeme und endliche Automaten.

14

B1.

+

SA Langlmaack (1971), 4 B1.

[M

5/3, p.51, Monoids, groups, and unary algebras

(~ourse?) notes related to automata theory (~cochard)

79

Section: Backwards deterministic and other special-algebras.

4 A-5-B1.

80 Normal subjects of an algebra.

5

A-5-B1.

81 Monoids, groups, and unary algebra.8 A-5-B1.

82 Cascade product of algebras. 10 A-5-B1.

83 6.

Cascading backwards deterministic algebras. 18

A-5-B1.

84 7.

Monoids as free h-algebras, and groups as free inversion algebras.

9

B1.

85 Lose Notizen 1 kl.Dossier

[M

5/3, p.5,9], Unary algebras and automata. Related to Ecochard 1972 Notes on unary algebras, and automata

- backwards deterministic automata

- groups as Onput algebras

- decomposition

- esp.cascade decomposition

Strongly related to (predating or accompanying) M.Sc.Thesis by Ecochard 1972?

Ueber

100

Bl.lose, unpag.Notizen

1

Dossier (darin gebündelt:)

Handling of physe-states,

5

B1.

Cascade decomposition. 16 B1.

Examples.

28

B1.

Input-full case. 6 B1.

A backwards deterministic. 5 B1.

Direct action autornata on input states..

( ? ) .

14 B1.

A

is (discont.?) product.. , 6 B1.

Direct action. 3 B1.

[AA 5 (vgl.M~4), p.321, Automata Theory Book Ch.VI (Old,

? ? )

95 Ch.VI, Design Algorithms for finite automata; Vervielfältigung m.hs.Korr.&Zusätzen. B1. VI-1 - ^VI-84

Notes on old ch.VI of automata notes

96 5. The complementation lemma for finite-state conditions. 3 B1.

97 ... ^{Lemma 1; Lemma}

^{2.. 10}

^B1.

98 5. Design algorithm relative to a condition-language.

2

B1.

99 Prenex(?) form for formulas in MT b4< 1. ^{5 B1,}

100 10. A

solvability algorithm for sequential calculus,

10

ausgew.

vervielf .B1, aus ~üchi/~andweber (1969

;

~ i b l . 15) lOOa

11

andere B1.

101

Lemma (prenex normal form). Bl. a-C

102

Lose, meist ungebündelte Notizen 1 Dossier [M 5, p.391, Kleenels rninimality problem and various notes on finite

Automata

103 Kleenefs Theory of regularity for non-coded automata. 6 B1.

104

Kleenels Minimality-Problem. 7 B1.

105 Unbetitelte Notizbündchen, 3

&

7 B1.

[AA 6, p.211, Stochastic autornata: Notes on Papers by others 106 Stochastic transition algebra. 5 B1.

107 3 B1.Bemerkungen i.Anschl.an Starke, Stochast.Ereign.& Wort- mengen,

~ 1 . 4-~(SA)

108

Einschlägige SA von ~.~rbib(1967), J. ~erny(1966), A. Salomaa (1965), P.H.Starke (1965-6)

&

~.~.~abin(o.J.), z.T.m.kl.Bem.

V.

Büchi

C AA 1

109 Notes, additions

&

corrections taken form the Automata theory

book manuscript; meist ungebündelt, unbetitelt.

1

Dossier

[ C ] C o n v e x i t y

...

[C 1, p.231, Matroids (closure spaces). Older material List of content, by W.Fenton.

1

B1.

Perfect closure spaces.

2

B1.

Closure spaces which ar of character

2. 8

A-5-B1.

Notes on isolated elements and derivatives - closure axioms in terrns of derivatives. 13 B1.

Minors of a closure space (~utte). 4 B1.

23 gebündelte Notizbl.

Meist ungebündelte Notizen

1

Dossier Systems of representatives

Matroids, binary relations, and Systems of representatives.

9

B1. + ⁴ B1.Beilage: SA Mendelsohn

&

~ulmage(1958)

Meist unbetitelte Einzelnotizen

1

Dossier The polyrityk y

:

Ix~Y!# 1 on

2M

1 Dossier meist ungebünd.& unbetit.Notizen, m.SA G.J.Minty, Graphoids Problem: 1)Find nec.& suf.conditions such that the vectors...

6 B1.

10

geb-Und.Notizb1.

[C 2, p.221, Closure spaces (work on book)

Kurzbeschreibung d.Inh. (v.~.~enton), Outline, (~inleitung).

4 B1.

Why closure spaces are so called... 17 B1.

Chap.1. Axiomatics of closure spaces - Closure operators, closed sets. 7 B1.

The principal sets of a space; the based complete lattice of closed sets.

11

B1.

Principal spaces vs.complete lattices..

2

B1.

Reduction of a closure space. 15 B1.

Cuts of a q.0. 6 B1.

Singulary Closure Spaces vrs.order relations. 17 B1.

Topological closure. 6 BI.

V-spaces. 19 Bl.(meist A 5)

Chap.111: Representation of complete lattices by sets. 14 B1.

flV-representable complete lattices. 20 B1.

Completion of partial orders.

1

B1.

Chap.111: Representation by sets

&

completion (embeding incom- plete). BZ.111 1-24 rn.zah1r.Einschüben

(~hap.

IV) Chap

. ^I1 . Binary relations and based clo sure spaces.

Bl.1-13, 27-44, m.zahlr.Einschüben Tychonoff s theore 4 B1.

The Cantor space

.~'2 8

B1.

g*. Discrete closure spaces. 9 B1.

10*.

Classification of closure spaces.

5

B1.

Complementation in the lattice of all q.orders on

A.

6 B1.

The closure-space of all I-reduced closure operators on A.12B1,

Closure spaces (~orts.)

The closure-space of all cl#osure-spaces on A. 8 B1.

Course: Finite and Discrete Structures.

5

B1.

Convergence in a closure space. 5 ^B1.

To..ly disconected spaces..7 B1.

Ngbh.Systems.

3

B1.

7

unbetitelte, gebünd.Bl.

The terminal character of order types, filters vrs.directed sets.

56

B1.

Literature remarks: R.L.Blair on Büchits "Representation of complete lattices by sets; SA. A.K. Steiner

(1966),

R.Sikorski

(1951,1952)

Meist unbetitelte & ungebündelte einz.Notizen 1 Dossier Universal Alpebras; Lectures Purdue

1963

The Closure spaces over an abstract algebra.

5

B1.

Chap.: Universal Algebras.

15

B1.

Construction of a free algebra... 8 B1.

Notes on 1somorph.Types of Algebras. 4 B1.

Versch.meist ungebündelte Notizen 1 Dossier Discrete spaces

Discrete closure spaces.

19

B1.

Nöterian spaces.

7

B1.

Relativly maximal closed sets of a discrete space. 11 B1.

Discrete lattices as ideals over a semi-lattice;

10

B1.

Ideals vrs.congruens of a semi-lattice... 4 B1.

Kleinere Varia 1 Dossier

[C

3, p.11, Algebraic closure spaces ( ~ r a p h theory)

166

Büchi & Fenton: Axiomatic theory of convex sets and the Stone Lemma (First draft of paper Bibl.31 sent to J.Comb.Theory, = ch.II+III of [F'enton-Ithesis). Xerokopie,

23

B1.

167

^{Büchi &} Fenton: Series-parallel graphs and _{K 4 ;} I1frist draft1I.

Xerokopie, 21 B1. [C

3,

p.ll]

168

Directed Graphs, series-parallel Graphs, and K4, by J.R.Buchi and W.E.Fenton.

27

vervielf .BI. ( = draft for paper in

1983) 169

The matroid of a flat in

v~(K)

and its dual.

25

B1.

170

("Goes with The matroid of a flat. .",~enton). 25 A-5-Notizbl.

+ 1

B1.Büchinotizen

+ 1

Bl.m.Bemerkungen v.Fenton zum Dossier.

[C

3,

p.43, Closure spaces

171

Chapter 11, Matroids Bl.1-2; Chapter 111, Convex closure and Parametroids B1.3-7; Convex-closure spaces B1.8-12; Parametro- ids.. B1.13-17; Independence axxioms.. The linear ajoined..usw.

B1.18-22

172

Material... included in Fentonts dissertation. 82 B1. A-5 Weitere A-5-Notizen (von Fenton nicht benützt?):

173

Using all axioms... 22 A-5-B1.

174

Wright graphs and Series-Parallel graphs and the Wheatston Bridge.

9

B1.A-5

175

Every Cirt const of two..

3

B1.

176

Relativation of a graph... 8 B1.

177

Wheatstone Bridges, Series-parallel graphs. 2 B1.

178 Duality; Problems... 14 B1.A-5 179 Ca.. Th.. 361.A-5

180

Ungebündelte A-5-Notizbl.

[C 3,p. 181, Notes on hyperspaces (Convexity)

1 Dossier Hyper spaces.

5

B1.

The operators S.A,s/A in the liear spaces. 4 B1.A-5 (=nligearll?:

Minors of a closure space..

10

B1. A-5

"'Good' bases in a matroidfl(Betitelung v.F'enton).

7

B1.A-5 In the linear case one can replace the circuit axiom..

2

B1.

!Rpivalent formulations of binary for linear closure spacesN (betit.v.Fenton) . ^{4 B1.A-5}

X as the largest property in closures of sets... 14 B1.A-5 Gebündelte Notizen A-5 ohne Titel, 16 B1.

&

4

31.

[C 3, p.21, Convexity theory

Independence of the Ca..th.Axiom. 16 Bl.

(llMost of this is in Fentonts diss

...")

Let K ko.. . divison ring.. . ^{4 B1.}

"Order in a convexity ~pace~~(v.Fenton betit.).

10

B1.

Notes on V,;. . ^{4 B1.}

Unbetit.Notizbünde1.

38

B1.

F a flat in

v ~ ( K ) .

4 B1.

Every flat is the flat pont(?) of some Lex.. 3 B1.

Ungebünd.Bl.

&

Dossierbeschrieb v.Fenton. 6 B1.

[C 3, p.441, Closure space notes connected with seminar (Spring 1981) 198 The proper arangement of this material..

4

B1.

199 Ideals of

a

a.p.o... 5 B1.

200 a~ =

<A,O

^C

any a.q.0.

20

B1.

201

For a set of systems Y/ . . . ²⁹ B1.+2 Bl. (unabhgg.?) [C], Convexity Theory (copies

to

Fenton and ~erge)

Cut sets and cocircuits (in

a

convex space S)

[~enton betit.: "Duality in a convexity space; lNicel convexi- ty spaces (in which Relatively maximal

=

maximal)". 7 B1.

"Example of non-isomorphic convexity spaces with some linear adjointn(Fenton) .

Minimaly generated Rinels are caps. ("~escriging Relatively maximals in

a

convexity spacev,Fenton). 3 B1.

"Regularity(?) in convexity spacesu(Fenton).

llConditions for convexity spaces to be equivalentfl(Fenton).

7 B1.

S '

... ^{Seon. 4 B1. +} B1.Problem.

[ D ]

D

e t

e

r rn i n a c

y

o f g a

m

e s and monadic theories

...

[D

1-3,

P.

271, Deterininacy of games (Bib1.15,18)

208 Büchi/Landweber: Solving sequential conditions by finite-state strategies (SA, 1969), m.hs.Bemerkungen

209 On the Presentation of Winning Strategies via the Cantor- Bendixson Method. 12 Bl.(von fremder Hand?; 13ib2.20a).

210-212 Druckfassungen m.hs.Korrekturen 213 Gordont s Lemma

-

Bar-Theorem. 2. B1.

214-215 State Strategies for I& -Games (~oznan lectures? 1975?).

Typoskript & Vervielf .m.hs.Korr., 20 & 21 B1.

[D

2-3, p.231, Notes on determinacy of

(B~(F,)-)

games Lecture on ~Tttwo swnmers)

216 Elimination of quantifiers using determinacy of games. S.Fran- cisco, Jan.

1974. 9

B1.

217 1II.Decision methods for monadic theories. 5 B1.

218 Generallize result on B1 ($d)-games..

.

^{5 B1.A-5}

219 Vereinz.Notizen, z.T.v.fremder Hd.

1

Dossier

. Borel & Souskin sets

220 Equivalent forms for

Fd .

^{8 B1.}

221 Borel and Suskin sets "over c=P(w).

6

B1.

222 Souskin =

V

3ore+.

3

B1.

p*:

223 11.0rder-vector-strategies for ~l(y#)-games.

224 5.The proof of the main lernma.

225 Kleinere gebündelte Notizen und Kopien von solchen. 1 Dossier

[D

2 (MT~), p.131, Lectures, 1974: Borel-Sets, Souskin-Sets, Games

~ounding/ F'ilters/ Borel & Souskin sets/ 13egularity/ ~arnes/

Applica-kion. .40B1.

The Cantor space 2.'

9

B1.

Condensed and scattered parts of a set.

14

B1.

Union of perfect sets.

5

B1.

Using the C.B.process, Scattered union. 4 B1.

The original CB-process. 11 B1.

Ideals

-

The ideal of founded subsets...

7

B1.

Versch.meist gebündelte A-5-Notizen

1

Dossier

[D

2, p.131, Games and deterninacy

234 Classifying sets of rationals...

235 Versch.meist unbetitelte, aber gebündelte Notizen. 1 Dossier

236 Einzel-Notizen 1 Dossier

Radofs lemma

237

Radols lernma. 23 B1.

The general Ramsey Theorem 238 General form of Ramsey.

239 Meist einz.Notizen (z.~.v.fremder ~d.). 1 Dossier Infinity lemmas

240 Relationships between some infinity lemmas. 5 B1.

241

Relationship between Ramseyts theorems Ri.and the fou?-theorem

F .

5

Blatt.

242 Ramseyf.s

~3 ^-)

Oriented-fou-theorem

^i,

Fou-theorem. 10 B1.

243 Quantifications may be restricted to strictly increasing functions. 3 B1.

244 Ramification lemma...Bl.l-6d

245 Speckerls Results on Ramsey-type theorems (u.a.?). 5B1.

246 Einzelbl.

1

kl.Dossier

247 Lopsided games. 7 B1.

248 F, A la Davis.

2 B1.

249 Davis:

F d j

games are determined. B1.O-5

250 Lopsided closed games - The cl... case a la Hausdorff.

4

B1.

251 Meist ungebünd.Einzelb1.

1

kl.Dossier [~aria, zu früherem gehörend]

252 Rado

=

inf.lemma...

9

B1.

253 Godi ~oran(?) April 1974. Xerox v.fremd.Hd. 9 B1.

254 Gordont s lernma.

11

B1.A-3

[D 3, Determinacy of games... (~ib1.26,28); p.241

Papers on Games and Determinacy

[Beschreibg.v.~rof.~iefkes], 2

B1.

I. State stragies for >d,Gb-games. 17 Bi.

II.Order-vector-strategies

fo BI(?& )-games. Xerox d.Hs. 31 B1.

The monadic theory of two successors. Zürich, Dec.1977. 7 B1.

Automaten als Gewinnstrategien für unendliche Spiele. Collo- quium ETH Nov.30,1977. 4

B1.

Using Determinancy of Games to Eliminate Quantifiers (Bib.26).

Vervidf., hs.überarb.

12

+

⁹

^B1.

=

Outline of Lectures to the Polish Academy of Science at Po znan, 1977

Winning State-strategies for Boolean-Fb-Garnes. ~yposkript/Ver- vielfältigung. 45 B1.

=

Fassung

9/1/81

des (sehr veränd.)~rt.Bibl.28!

Order-Vector Strategies in ~l.(~,)~ames. Vervie1f.m.kl.h~.

Korr.

22

B1.

[ G ] G r a p h s

---

[G I, ~ ~ 1 9 3 , Jordan Circuits a

X g a r d )

263 Definition of graphs.

24

BI.

264 Examples. 6 B1.

265 Meist ungebündelte und unbetit.Notizen

1

Dossier

Embeding of Graphs into 2-manifolds. Haggard,

1966- 266

Outline(?). 7 B 1 .

267

General -form of McLanes Theorem. 12 B1.

268

Meist ungebünd./unbetit.~otizen

[G

1,

P.

321, 2-irreducible graphs

269

Problems.

6

B1,

270

^Let

G

be imbeded on T2..

9

B1.

271

Process 1-

.

^{8 B1.}

272 Def.:

C

a circuit of G..

6

B1.

"Algebraic closure spaces (and ~ r a p h theory)"

(~etitelung v.l;'entons ~ a n d )

273

Graph theory

-

Kirchofffs Laws,

19

BI.

274

The number of binary matroids

-

Modular closure. 12 B1.

275

Conjugate pairs(?) as bi-partite graphs with circulation(?).

3

B1.

[ L ]

L o g i c a n d M o d e l T h e o r y (L 1, p.261, Elementar~ theories. Notes & class notes

Michigan, Illinois, Purdue

Elementary Theories. Lecture-notes, Illinois 1955/56.

86

B1.

Logic-Seminar Ill., I.sem.1955-56: First order Predicate Calculus

.44

B1.

Logic Seminar Ill., I.sem.1955-56: Algebraization of Predicate logic. 21 B1.

Logic Seminar I.sem.1954-55: Organization...

4

B1.

Löwenheim-Skolem-Gödel Theorem. Logics Semi.1954-55. 11 Bl.

+ ⁵

^{vervielf .BI.}

Logic Seminar (Xich.), 2nd.sem,1954-55. 28 BI.. . Michigan

1954(55?)

Lectures in Metamathematics.

190

B1.

(189-90

Class list).

9

2. Primitive recursive functions.

24

B1.

9 ^3.

General Recursive Functions. 5.th week.

45

B1.

Notes on predicatecalculus & elementary theories

Logic Seminar, Purdue, Sept.63: Elementary (i. e. Ist order) Predicate Calculus. B1.1-12

Elementary Theories. 18 BI.

Cantor-Bendixson. 10 B1.

The Tarski-Lindenbaum algebra..

4

B1.

A method (Compartness, Skolem-Löwenheim.

.

⁾

.

^{18 B1.}

Versch.z.T.gebünd./beät.~otizen 1 kl.Dossier [~aria am Dossierschluss: ]

A

natural partial order on Qp... 20B1.

0-notations..

.

^{15 B1.}

Every rel.system

D... 4

B1.

[L 1/21,

Logic

I

[L

11, Exzerpte? und Notizen

293 Models of Lo~ical Svstems: John G.Kemeny...

36

S.

294

Skolem: ~ichtcharakt. d. zahlenreihe

-

^{~ b b .} einer Menge,. 4 BI.

294a Versch.kl.Notizen 1 Dossier

Logic

I (1968?)

Präliminarien.

11

B1.

Chap.1. Model-theory of elementary axiom systems. Bl.1-12 Affine plane geometry..

. ⁹

^B1.

The elementary gheory of dense linear order.

3

B1.

Elementary aproximations of Peano s Axioms.

14

B1.

Set Theory. 12 B1.

Elementary axiomsystems and the model-relation.

16

B1.

Gödel's Completeness Theorem.

Completeness of weak second order pred.calculus.

The Skolem-Gödel-Herbrand proof...

30

B1.

Totally free algebras of terms.

9

B1.

The fundamental problems of elementary model theory. 8 B1.

~ersch.~ebünd./betitelte kl.Notizen 1 Dossier Logic I1

Hode1 theory.

39

B1.

Elementary theory of abel. groups without torsion.

. ³⁰

^B1.

Quantif.elim.inZ.. 11 B1.

C. The basic properties of ultra-products. Xerox d.Hs.

15

B1.

~ S c h l u ~ s v a r i a ~ ~ (Programm 1965, Einschreibungen 1972?,1977, versch.einz.Notizen., grosst.gebündelt. 1 Dossier

[L

3, p.251, Lecture Notes. Gödel's Incompleteness Theorem

313

Nach- oder Abschrift (von ~entons?~and). 109 B1.

314

^Gödelt s theory of incompleteness of formalized proof-theory.

88 B1.

315

SA Shepherdson

(1959/60)

& Feferman

(1960) [L 4,

p.251, Set Theory Notes

I +

^I1

Set Theory. Lecture notes, Purdue

1965-66

317 Seminar.

3

B1.

318

A system for ordinal notations.

6

B1.

319

A system of notations for recursive sets. 12 B1.

320 Lectures on set-theory; outline..

.

^{8 B1.}

321

Th.2.., Th.3..

13

B1.

322 Gödel, The Consistency of the Continuum Hypothesis

(SA 1940),

m.Bemerkungen und Notizbl.

1

Dossier 323 Gödel, The Consistency of the Axiom of Choice.. (SA 1938),

m.Bemerkungen & Notizbl.

324

Varia: SA Fraenkel (1922), Cohen (1966); & meist gebünd.

Kotizen 1 Dossier

[L

5, p.221, Equational Theories. Notes

-

325

Equational extensions of Group theory

[A 3,

p.181. 39 B1.

Totally frei Algebras

-

Transition algebras with multi-ary Transitions

-

Calculus of Equations

326

Free Algebras.

13

B1.

327

Notes on the free algebra with one generator and one binary equation.

7

B1.

Generalized Artithmetics with one origine 0 and a binary generator.

5

B1.

Presentation of Algebras. 4 B1.

Einzelnotizen

1

Dossier

Calculus of Equations. 10 B1.

+

Beilage: Vervielf.C.C.Elgot (19571,

15

Bi.

Associative equational theories. 20 B1.

Algebraic dependence in Rings.

13

31.

Equational classes over Group-theory; z.T.gebünde1telbeti.t.

kleinere Notizen

1

Dossier

[L 6?,

p.191, Galois Theory of Element.Systems

PP- - -

335

Z.T.gebündelte/betitelte kl.Notizen

[L

6-8, p.201, Model Theory

1

Dossier

336-338

SA i"si.isiorley 1963,1965,1970, mRandbemerkungen und Zusatznotizen

339-341

SA Svenonius

(1959)

* J.Keisler (1961), R.M.Robinson (1951), m.

Randbemerkungen & Zusatznotizen.

342

PIeist ungebündelte, ungeordnete? A-5-Notizbl. 1 Dossier 343-351 Plato solids

-

Robinson's Theorem

-

The terminology of stone

spaces

-

Relatively categorical theories(Berkeley, July 8,

1963

(m.SA., ~ibl.ilbst.9)

-

Dependence of types over a theory

-

u.a.unbetit.Bünde1ungen. 1 Dossier

352

Versch.meist unbetit./ungebündelte Notizen

1

Dossier

[L

? ] , A Fundamental Concept in the Theory of Models (~bstraction)

353

^{Arbeit in.} Jesse B.'rJright (Logic Session, Ann Arbor

1955

Aug. )

,

ua. 24

BI.

354

On Hierarchies of mathematical theories. Notre Dame, May

55.

13

B1.

355

Invariant theory

in

groups. Chicago, April 22-23,

1955.

34 BI.

[L 7-8,

p.191, Work with Danhof (~ib1.20-22)

356

Model theoretic approaches to definability. Revised Version.

Bl.1-18 rn.hs.Korr., vervielf.

357-358

Definibility in Normal Theories. Vervielf.m.hs.Korr. ~1.1-11 &

- - - - - - Bl. 1-12

359

Variations on a theme of Cantor in the theory of relational structure. Bl.1-33

Bandschr.Notizen:

359a Languages with well-founded depth of quantification.

5

B1.

360

Galois Theory.. 20

BI.

361

(Definitions and theorems as moduls

. .

⁾

^,

^B1

^{. l-4b}

362

Scott formula. 8 B1.

363

Parallel development of Separation and definability theorem..

14

B1.

364

Unbetitelte, meist gebünd.Notizen 1 kl.Dossier

[ M T ] M o n a d i c T h e o r i e s

...

[MT 1,

p.291, Weak Monadic Theorie~ (~ibl.7 +13)

P

365 3.The weak second order theory of a 2 , < k

16

B1.

366

Prenex normal form of sentences in ~2(d ,C).

4

B1.

367

Undicidability of

WT ... ³

^B1.

368

Extension to general ized arithmetic.

13

B1.

369

l,...

,

¹

. Z

370

Review v.&ob . ~ c ~ a u ~ h t o n . 10 vervielf .BI.

371

Kl.Notizen, meist betitelt/ungebündelt. 1 Dossier

[MT

2, ~ ~ 1 3 , 2 3 1 , Monadic Theories & Closed Cofinal Sets of Ordinals

372

Meist gebündelte, aber unbetit.Notizkomplexe 1 Dossier

373

Z.T.gebündelte/betitelte Notizen, meist A-5 1 Dossier

374

Confinal Sets.. z.T.gebündelte/betitelte Notizkomplexe, m.

SA. Sikorski

(1949).

1 Dossier

Notes on Monadic Second Order Theories

375

. . Notes and problems on monadic second order theories.

14

B1.

376

Standard and non-standard models

.

377

Kl.Varia, z.T.gebündelt/betitelt.

[MT 2, p.321, Monadic Theory of W. Notes

1 Dossier

378

Lecture on Tarkils Problem L.of Comp.Group, May 13,1960.

Bl. la-10

379

Entscheidbarkeit der elementaren Theorie der Addition von Ordinalzahlen und endliche Automaten. B1.1-11

380

On the unse of finite state recursions in the theory of ordinale. Case Institute lecture

1965.

8 B1.

381

Design Algorithms. Bonn, Juli

1962.

Bl.1-13

382

Sequential operators

-

Design Algorithms

-

Winning strategies

-

Sequential games..(1960/ Zürich, April 23..).

13 B1.

383 Varia, z.T.betitelt/gebündelt

1

kl.Dossier

384

Solving of conditions in sequential calculus (Jessels Proof

of Wangls result).Z.T.gebündelte/betitelte Notizen.1 Dossier

[MT

2, p.51, Games and desciption set theory used for decision procedure

of #T (wl)

385-386

Z.T.gebündelte/betitelte Notizkomplexe und Notizen, mit SA.

Saarnio

(1968).

2 Dossiers

[MT

2/3, p.271, Monadic Theories (~ib1.8,14,17,23,24,25,27)

387-389

~üchi/Siefkes: The Nonadic Second Order Theory of All Count- able Ordinals

-

Büchi: On a Decision Method in Restricted Second Order Arithmetic

-

~üchi/~iefkes: The Complete Exten- sion of the Monadic Second Order Theory of Countable Ordinals.

Publ.m.hs.Korr.&Zusätzen.

390

Lecture on SC: Finite Automata & Decidable fragments of second order a&hmetic. Madison, May

1969.

Bl.la-8

391 Analysis of definability in SC. Robinson's Conjecture. 8 B1.

392 SC

= the theory of binary expansion of reals.

11

B1.

393

Undecidability of [0,s1,S2

...I -

^{A Coding of}

^the

^system

@Hz,

SI. .. ⁶

^B1.

394

Kleinere, meist ungebünd.Notizen; Review R.Mc.Naughton.

1

Dossier

[MT 4,

p.391, Sequential Conditions

- P- P P- P-

Notes on Churchts Seminar, Illinois.

47

vervielf.& handschr.

B1.

Church: Appl.of Recursive Arithm.in the Theory of Computers

& Automata. ~ervielf.(l958), rn.hs.Erg.Büchis; ca.70 B1.

Hao Wangts Result, Jesets Proof. 20 B1.

Design Algorithms. Meist gebünd./z.~.betitelte Notizen;

SA;C.A.Elgot

(1958).

1 Dossier

Truth-tables for Prop.Calculus.

86

B1.

SA.Alonzo Church(l954) m.2 hs.Beispielbl.Büchis.

Truth-tables: z.T.gebünd./betit.~otizbl. 1 Dossier [ Q ] Q u a d r a t i c F o r m s . . .

[Q 1, p.5], Words on the Alph. $1.21 and quadratic form~. Lecture Notes, F'all

1979-80

402 Words over the alph. [ l,21 and quadratic forrns, (m. 1nh.verz. )

.

262

S.

403

Related Work Notes. Darunter einige gebündelt/betitelt

2 Dossiers [ Q 1, p.441, Research Notes

Quadratic Forms, Unimodular matrices, Words in two symbols (Well bevor the Fall

1979

~ecture)

404

Zum Teil gebündelte/betitelte Notizen 2 Dossiers [Q 1, p.121, Quadratic Forms

405 Zum Teil gebündelte/betitelte Notizen (Da geordnet erschei- nend, in der vorliegenden Folge neu durchpaginiert).

15

7 B1.

406

Gebündelte Notizen, meist A-5 1 Dossier

407

Ungebündelte Notizen, meist A-5 1 dickes Dosser [Q 1, p.161, Quadratic Forms

(From Tablet und blackbord)

407

Durch Verzeichnis erschlossene Notizen,

189

B1.

408 idem, 215 I31.

409

Schlussvaria 1 kl.Dossier

[Q 1, p.181, More material on qadratic forms

On floor below blackbord; Much on words, Atoms, Factors of 410 The S,trong? of symmetry.

31

A-5-B1.

411

Finding all the 1, such that p/pl..

6

B1.A-5 412 Quadratic Forms.

15

B1.

413 The abvious factors of

(2

1

-1).

10 B1.A-5 414 The abvious factors of tl,sl...

21

B1.A-5

415 Solutions of Zell?-equations and its mate.. 10 B1.A-5 416 The periods of D=1+4 d special.. .

¹²

^B1.A-5

417 Gebündelte Notizen

A-5

1 Dossier

418

~ngebündelte/unpaginierte

Notizb1.A-5

2

Dossiers

[ Q Z ,

p.443], Carton with notes on quadratic forms, minor data matrices, words in

2

symbols. Given... bevor the fall 1979 lecture

419 Pell equations, Reduction of Quad.Forms 1978: meist ungebünd. / unbetitelte Notizen

A-5

[Q 1, p.61, Markoff number

420

Markov Nwnbers.

28

B1. A-5

[Q 1, ~ ~ 4 4 ~ 1 , Folder (old) on Pell equations, related to 5 squares problems. Given. . . ^{summer 77}

421 Meist gebündelte Notizen. 51 (b.d.Archivierung paginierte)~l.

422

idem; 76 B1.

[Q 21, Words

&

S squares

423 Zum Teil gebündelte Notizen (rn.Kurzinh.; b.d.Archivierung in der vorliegenden Reihenfolge paginiert). 44 B1.

[ Q 21, H.10. and existential sentences

in +,Q 424 idem, 74 B1.

[ Q 2, p.121, S squares ( ? )

Squares (mod.9). . .

¹²

^B1.

Reduction-Theory .

The solutions of X~-B~;~+Z~=~. ^{6 BI.}

x2-dy2=1. 6 B1.

~xample:~2= -5. 11 B1.

9¿ =

A.. . ^, 1) a comutative ring.. 6 B1.

Con.. and normal sets of a Hoop.. 6 B1.

The degenerating quadratic case. 3 B1.

Gebündelte, aber unbetitelte? Notizen, A-5.

1

Dossier Mit ungebünd.Rest

Q

X

4 +1=0.

10

B1.

q2-2

z2 +

^{~2 = 8}

¹ . ^{6 B1.}

d

=

16(32)..

Problem: For matrices define...

8

B1.

Problem (Gaschütz, Kiel) ... ^{16 B1.}

Unbetitelte Notizbündel, meist A-5 1 Dossier

Ungebündelte Notizen, meist A-5.

1

recht dickes Dossier

[ R ] R e c u r s i v e F u n c t i o n s

...

Undecidebility

[R 1, p. 281, Turing-Machines (~ibl. 9)

441 Bibl.9,

11Turing-Machines.."(1962).

Proof Copy m.hs.Zusätzen 442 Turing-Machinen und die Nichtexistenz gewisser Entscheidungs-

verfahren der Mathematik. Kolloquium Main, Feb.8,62; Saarbrük- ken. 16 B1.

443 The action of a Turing-machine as a predicate-recursion. 5 B1.

444 Notes to the Domino-conjecture - Reduction to

C43v]

of Domino with boundary-condition on one axis. 4 B1.

445

~ovability/~nsolvability

... Zusammenhang zwischen Skolem- Löwenheim. 2 B1.- 3 Bl.(p.6-8) -

¹

^B1.

446 Consistent sentencea VJ1 VVV without recursive model. 24 B1.

447 Mostowski, A formula with no recursively enumerable model.

SA (1955)

&

6 B1.Ergbl.Büchis

448 Schlussvaria.

1

kl.Dossier

S.a.einschläge Korr.:

AlonozoChurch (1961), ~.Dreben(l961), P.Bernays (1961),

A . S .

Kahr (1962), G.Köthe (1961-2), J.Suranyi (1961/5), S.Tennen- baum (1962), Hao Wang (1961-2).

[R 2, ~ib1.29,30]

- - -

449 Büchi,Mahr,Siefkes: Recursive Definition..Sent to2.Frege Conf..

23 B1.Xerokopie.

[R 3, p.391, Computability

450 Recursion Fwiction Theory.

⁸

B1.

451 Notes on variants of (T~). 2 B1.

452 Turing scaner... B1. -1 - ⁴

453 Notes on Galvis-connections and closure operators. 9 B1.

454 Equational theories.. .

⁸

^B1.

455 Set Theory...lO

B1.

456 Rectangular and Equivalence relations. 7 B1.

457 *-depth of regular expressions... 4 B1.

458

General minimality. .. theory for relational Systems.

8

B1.

459

~l.gebündelte/z.T.betitelte &

Einzelnotizen. 1 Dossier [R 3, p.391, Computability. Varias

460 Creat.-complete Standard Enumerations of rec.enum.sets. 22 B1.

461 New Proof of Gödel-theorems 462 Uniformity theorems...

⁸

B1.

463-465 Kommentare v.Büchi zu ~.~.Post(1946 - E.A.Moore (1952; Typoskr.

kopie v.~.~.Davis/C.E.~hannon (0.J.). 5 + 6+4 B1.

466 Review of "Automata Studiesll by Büchi/~lgot..&c. (~niv.of

Michigan. 9 vervielf .BI. ( ~ u l y 3,1957).

[R 3, p.14,38,39], Recursive functions

467

Proof that all recursive functions are Turing-computable

-

Implicit Definitions

-

Remarks on solutions of recursion- conditions.

7

B1.

468

The theory of deductions. 10 B1.

469

^Problems

-

Recursiveness of the E-operator

-

Recursion rela- tive to partial well-ordering

-

Die Iterationen der Addition.

24 B1.

470

Predicate recursion.30 Bl.(z.T.Seminar-~otes).

471

Relative Predicate-Recursion... Generability,..

27

B1.

472

Predicate-Recursion.

43

B1.

473

Notes on Predicate-recursions...

25

B1.

[ S I

S u b j e c t s

...

[S

0, p.401, Old Problems

P-- P- -

474

Vektortheorie.

54

B1.

475

Neuer Aufbau der Vektoralgebra. 11 B1.

476

Ideen. 24 B1.

[S

11, Doctoral Dissertation

(B

1)

477

Dissertation, mit hs.Zusätzen.

478

P.Bernays, Gutachten über die von Herrn J.Richard Büchi...

eingereichte Arbeit.. u.a.

6

B1.

479

Pointfree spaces

-

The representation problem... Complete Boolean Algebras

-

Homomorphismes... The Choice Principle...

40

B1.

[S 21, Representation of lattices

Papers G.N.Raney

(SA

1953, ~yposkriptkopien), m.hs.Bemerkungen

Büchis

.

^{1 kl .Dossier}

Connectionship beween meet- and join-irreducibility. 3 B1.

Charakterisiere diejenigen completen lattices... 10 B1.

Homomorphe Abbildung von set-lattices.

4

B1, Verallgemeinerung der Theorie. 8 B1.

Lattice aller congr.rel.einer Algebra. 9 B1.

Klassifikation aller Ketten.

4

^B1.

Rings which are sub-direct unions of fields. 5 B1.

Die Struktur abzählbarer Bollescher Ringe.

6

B1.

Schlussvaria, z.T.betitelt/gebündelt. 1 kl .Dossier Representation of Boolean Algebras

Equivalence of Stones Repres .Theorem with the Axiom of choice.

4

B1.

Separabel Boolean Rings. 8 B1.

Some density-concepts in partial orderings.

7

B1.

Conjugate Elements of a Boolean Algebra...

15

B1.

Let D be maximal relative...

4

B1.

Versch.(zum kl.Tei1 gebündelte/betit.)~otizen. 1 Dossier On the representation of Boolean rings by sets.

78

(b.d.~rch.

pag. )B1.

[S

2, p.401, Representation by sets

-

Galois corrections Galois-Connections, Homomorghism U. a.

55

31.

Charakterisierung derjenigen 3001.6-Algebren die Xengen e ~ l - gebren sind

-

classification of operators on relations

-

^The

Drive-graphe

-

Cuantsnmathernatik.

58

31.

Konforae Abbildung von ebenen Gebieten und ihre Charakterisie- rung mittels*-Klassen

-

Char.der Diff-baren Kurven mit Hilfe von Xaxirnalerl

4

-Klassen..

.

Orthogonality.

. . ⁴⁶

^B1.

Die Xethode der reellen Funktionalen _{C ( X )}

-

^Prädikate

-

^Eine

allgemeine Strukturlehre

-

Points and Ideals of subsets of a space a.0.

87

31.

Topo1.3001.Algebra.. Gefüge.. Cornplete Extensions of a Boolean Ordering..

. ³³

^81.

SA ~rätzer/~chmidt(l961) m.hs.Erg.Büchis. 21 B1.

Begriffe, Exzerpte u.a.

14

51.

Various Kotes, zumeist ungebündelt/unbetitel. 1 Dossier

1

^[S

^3-41,

Axion o f choice

-

Totally heterogeneous spaces

505

Set Theory [S 3,p.39].

506

Auswahlprinzip

-

Heterogenität.

60

BI,

1

^[S

^51,

3üchi-Owens: Skolem Rings. Complenented Dleroids & Boops

507

Older version of Owenfs Ph.D.Thesis IfVarieties of Skolern Rings'

1974.

Vervielf., 81.1

- ^5.2.7

508 Büchi-Owens, Ukoleri Rings liotes C% Corrections.

78

211 .A-5

509

id., ;Is 1975, m.hs.Zusätzen.

55

B1.Vervielf.

+ ⁶

^iYiSs.

510 Büchi-Owens, Complemented Nonoids and Eoops.

34

31. hs. korr.

Vervielf.

- - - - -

[S 6 , p.61, Implicative Soolean Algebra

511

Representation of inplicative Boolean Algebras. Korr.Typoskr.

12

31, ?X 34 Sl.Notizen A-5 hierzu.

512 1mpl.Boolean Algebra.: Representation of 1mpl.B.A. 28 B1.

513

SA A.H. Copeland (l950,l953,l954)

514

Notes on Countable I.B.A.ls.20 B1.

,515

I.B.A.

62

31. (gebündelte, b.d.~rch.durchpag.~aria)

.

516

Zum T.betitelte Einzelnotizen

1

Dossier

[ S 6, p.391 Measure, Probability

517

Law of large nunbers a.0.

27

B1.

Ordinals...

518

The tail relation on ordinals

-

Iteration and critical members of a set V

-

Cofinal subsets of wl

-

The operator Q

-

^Schub-

fachprinzip for ordinals.. a.0.

51

B1. (b.d.~rch.durchpag. _).

519

Rare sets, scattered sets and the ideal 0..

-

Iteration of operators of type 2

-

Lemmas, Remarks..

83

B1.A-5 (i.d.vorl.

Ordng.b.d.~rchiv.pag.)

520 Zum T.gebündelte, z.T.Einze1-Varia 1 Dossier ( e i n s c h l . ~ ~ Sikriski, ca.

1950)

[W

1, p. 41, Word and early notes on Thue Papers

521

Kopien v.Arb.Axe1 Thues (1906,1910 und

1914)

m.Bemerkungen Büchis &

14

3l.h~. P:otes on Papers by Axel Thue.

[W

2, p.71, Notes on Tdords (free semigroup)

Possibly related to arithmetic and finite automata. Worked on with Steven Senger summer/fall

1982

522(5)~hue c&s and sequences.

(W

2,p.7) 1 kl.Dossier A-5 523(1)~emark on strong coes and presentations and submonoid existen-

tial definability. 1

B1. (W

2,p.7)

524(2)Types of Presentations. (do

.

^{) 1} kl.Dossier A-5 525(4)More on ATmls and presentations U com V... 1 kl.Dossier A-5 526(7)More on Thue sequences and derivations.(~ 2,p.7) do.

527(8)Finding solutions via productions

-

Related productions on Length of words. (do.) ¹ kl.Dossier A-5 528(9)Notizen zu: Decomposing equation into system. 3 ^B1.

529(3)

^{11 :} Counting number of ATmo on Level e of tree.

(T;:

2, p.7) 1 Dossier A-5 530(6)Notes on Words. 1 dickes Dossier A-5 (m.~nhaltsverz.)..

[ ~ d 2 , p.43], Codes, Presentations of ~ords,3 -def.

Buchi Notes July 4,

83

531(1)~ome existential definability remarks. 1 kl.Dossier A-5 532(2)From study of overlap and division orders. 1 Dossier A5 533(3)Codes and related problems

-

Leads up to Thue codes. do

.

[V

3, p.121, Definability.., p-function..

534

Notizen betr.bfunction on words, Recursions, Coding a.0.

1

aossier

[W

3, p. 4b2], Median Algebras

535

Median operation on Trees.

44

51.

536

The free median algebra on two generators. 10 B1.Typoskript- kopie

+ ³⁴

Bl.meist A-5-Notizen

[W

3, p.431, Arithmetic of Words

Old notes on Hilbertts 10-th and the corresponding word problem

537

Einige Begriffe in der Arithmetik der Wörter.

4

B1.

538

Idempotent elements in finite semi-groups.

6

B1.

539

A lead to Hilbertfs 10-th.

6

51.

540

Remakrs on Diophantine predicates... Bl.1-8

541

Quaternions.

7

31.

542 Varia: z.T.gebündelte/betit.? Notizen

1

Dossier

[V 1,

p.

1,371,

Diplomarbeit

543 Differentialrechnung in abstrakten Räumen. Srosch.,

103

p.

544 Zum Richtungsraum. 5 81.

545 Funktionenräume. 21 Notizzettelchen

546 Ueber die Verallgemeinerung in der Mathematik. 3 B1.

547 Weiterführung der Theorie.3 B1.

548 Einzelnotizen ("~roblerne~~ u.a., d.Dip1.-Arbeit lose beigeleger 1 Dossier

549

Typoskript-Kopie & Xotiz.

6

I31.

[V 3,

p.jg], Folder "Logic of Sense and Den~tation~~ (Church)

- -P- P P P P- P

550 SA Church (1951) m.Xarginalien & Kotizzetteln. 1 Dossier Unbezeichnete Varia

Notes on Finite Nath. Course. Notizen A-5 (einige wenige ge- bündelt/betitelt). 1582/3? 1 Dossier Xotes l r o n books

Aus J.v.lieumanns islath.Grundl.d.Quanten-;.lech. 1 kl.Dossier

Anderes do

.

Notes out of Ikngenlvhre by _-

F

.Hausdorff (1944) do

.

Taken out of Diophantine uquations, L. J.>qordell. 1 Dossier Fron The calculi of Lambda-Conversion, A.Church. do

.

Removed from Riff erential &. Integral Calculus (~andau)

.

^do.

Taken out of Sook idieasure Theory, ?.R.Halmos 1 kl.Dossier Peng-Siu Xei Thesis. Typed Ms,

rn.

gel .Marg.Büchis.

152

B1.

"Axionatic Theory of Linear and Convex Closureff

R.Fraiss6, Une Hypathese sur llextension des relations finies et sa verification dans certaines classes particulikres.

31

vervielf.3l.m.geleg.Notizen Büchis.

Sernays, A System of axiom.set theory I1 (1941), m.7Bl.Notizer Büchis

SA

~irkhoff/~rintr, Repr.of Lattices by sets

(1948)

E.W.Beth, On Padoif s Method.. (1953)

Juris Hartmanis, On the Lattice of Topologies (1958), id., Lattice Theory of generalized Partitions (1959)

P.

Crawley, The Isonorphism Theorem in comp. gen.1at-t. (1959) B .Eushnik/~. ~.>:iller, Conc. Similarity Transformations of Linearly Ordered Sets (1940)

H.S.Leonard/~~.Goodman, The Calculus of Individuals & its uses (

1940)

M.Davis, Infinite Games of Perfect Information

(1964)

(alle mit Plarginalien/~otizen Büchis)

Betr. Turing-Xachines.XS-Kopie V. frd. Izd. e< Xerox

F. C.

Hennie (1966). 20 B1.

(17-19

orig. ) & Xerox S. 35-41

SA J.Xright, Quasi-projective Geometry of two Dimensions (1953-4).

D.HensZey, Sequences of Squares with second difference of 2 and a problem of logic, SA. m.Büchi-Theorem. 8 vervielf.Bl.o.2

Nachtrag März 1986 Varia

573-575 Referate: Typoskriptkopien A-Z, Korrekturabzuge 3 Dossiers

US AAr-Fgrce, ~ ~ ~ e - A ~ r - D e v e l o p m e ~ t ~ C g n ~ e ~ , - P r o ~ o ~ a ~ s

(1962-)

- - - -

576 ^{Jesse B} Jright, Mathematical Automata ~ h e o r ~ ; Kopie 19 B1.

577 ^J .B. Wright & ^J .R.Buchi, Math. Automata Theory. Kopie 20 B1.

578 J.R.Büchi, The Theory of Automata and Behavior Languages, Kopie 21 B1.

579 Budget 1964-1967, 2 ~l.(~opie) 580-612 Korrespondenzen hierzu, 1962-4

613 Notizen aus: Hilbert/~ernays, Grdl.d.Math.Bd.1-2 1 kl.Dossier

614 Entwurf einer Prüfungsaufgabe?

1

B1.

K o r r e s p o n d e n z Bw: Briefwechsel

betr. : die genannte Person betr.Korrespondenz an Bü.: Briefe an Hrn.Büchi Bü.an: Briefe Büchis an die

genannte Person

Büchi

Briefregister

~

A

d d

i s o n, John Bw.

Math. -Prof. 1963-5 Univ.California, Berkeley

A 1

C

a

1

a y, David

Mathematiker New York A

1

- D h a h i r, M.Wassi1

Math. -Prof.

Univ.Kuweit

an Bü.

1964 Bw.

1977

~ ^{A m i t s}

^U

r, Shimshm Bw.

Math. -Prof. 1979

Hebrew Univ.Jerusalem

A n d e r s o n, Gilbert Bw.

Chefbeamter (State off. 1961 educ.exch.)Wahsington

A s s e r, Günther

Math. -Prof.

Greifwald

Bw.

1978-81

A

X

t, Paul Bw.

Math. -Prof. 1969

Pennsylvania State Univ.

Pennsylvania

B

a

e r, Reinhold Bw.

Math.Prof. 1954-55

Univ. Illinois Urbana

B a r - ^{H i 1 1} e 1, Yehoshua Bw.

Math. -Prof. 1963-65 Hebrew Univ. Jerusalem

B a r t o o, James B. Bw.

Math.-Prof. 1963

State Univ., Pennsylvania B a s s, Leonard

J.

Computer-Wiss.

Riverside Ca.

Bw.

&

betr. 35- 47

1967-70

B a s

s

i, Achille Bw.

Prof .Esc. de Engenharia 1955-56 Sao Carlos (Brazil)

B

a

^U e

r, Friedrich L.

Math. -Prof.

Univ.Mainz

Bw. 51- 65

1960-63

B e ck e r, Joseph an Bü.

Mathematiker 1977

Purdue Univ. Lafayette

B

e

1 a, Ramon Bw.

Dir.Comm.Educ.Exchange 1961-62 Madrid

A

r a n a, Luis J.de Prof .Dr, Ing.

Bilbao B

e

r n a y s, Paul

Math. -Prof

.ETHZ

Zürich

B i

b

e 1, Wolfgang Bw.

Mathe-Prof. 1971

Wayne State Univ. Detroit

B i e r i, Hanspeter an Bü.

Dr., 1nst.angew.Mathem. 1977 Univ.Bern

B o e r g e r, Egon (*1946) Mathe-Prof.

Univ. Salerno

an Bü.

1973 B o h

1 k

e n, Herwart Bw.

Zoo1.-Prof.Univ.Kie1 1973

B r a

U

e r, Richard Bw.

Mathe-Prof. Harvard Univ. 1955-56 Cambridge

B r u n n e r, Johann an

BÜ.

Primarlehrer St.Gallen 1943 B r u n n e r, Norbert an Bü.

österr.Mathematiker 1981 B r

U

n s, Günter

Mathem., Berlin

an Bü.

1960

B u

d

a

C

h, Lothar Bw.

Mathe-Prof. Univ. 1978-1984 (Ost-)Berlin

B

U

r

k

s, Arthur Bw.

Math. -Prof. 1958-1963 Univ.Michigan

Ann

Arbor u.a.

B

U

s

^C

h, D.R. an

Bii.

Mathem. 1967

Univ.Canterbury

Christchurch, New Zealand

C a i a n i e l l o , E.R.

Phys. -Prof.

Univ.Neape1 C a i r n s, S'tewart S.

Mathe-Prof.Univ.111.

Urbana C a

p

k a, Dave

Mathe-Absolvent

0.0.

C a r r, John W.

Prov.Univ.Pennsy1vania Philadelphia

C h r

i s m a n, Carol S.

Math.

Northern 111.Univ.

De Kalb C h

U

r

C

h, Alonzo

Math. -Prof.

Univ. California Los Angeles C 1 a r k, Allan H.

Mathe-Prof.

Purdue Univ.

Lafayette C

1

e a

V

e, John P.

Mathem.

Univ.Southampton C 1 o t e, Peter

Mathem.

Univ.Paris C o n t e, Samuel D.

Prof .Comp.Wiss.

Purdue Univ.

Lafayette C o r c o r a n , John

Mathem.

State Univ.New York Buffa10

C r a

i g,

William

Mathe-Prof.

Univ. California Berkeley

U. a.

C

U

m m i n

g

s, Willis

A.

Editor

b.

McGraw-Hill

Bw.

1963-64

Bw.

1957 an Bü.

0.J.

Bw.

1968 an Bü.

1974

Bw.

1957-68

Bw.

1964-82

Bw.

1963 Bü . ^an

1983 Bw.

1963-77

Bw.

1982-83

Bw.

1957-63

an Bü.

1962

New York