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Exercise 3 Construct infinity axioms in the classes (i

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Lehr- und Forschungsgebiet

Mathematische Grundlagen der Informatik RWTH Aachen

Prof. Dr. E. Grädel, F. Abu Zaid, W. Pakusa

WS 2011/12

Algorithmic Model Theory — Assignment 3 Due: Monday, 7 November, 12:00

Exercise 1

In the lecture DOMINO was defined as the class of all domino systemsD which admit a tiling of N×N. Show that DOMINO is co-r.e..

Hint: Construct a tree whose nodes are tilings of finite squares and use König’s Lemma.

Exercise 2

Let Π ={∃,∀}≤k be the set of all quantifier prefixes of length not larger thankfor some fixed k and p afinite arity sequence (i.e.Pn≥1p(n) is finite). Prove that Sat([Π, p,(0)]=) is decidable.

Exercise 3

Construct infinity axioms in the classes (i) [∃∀2,(0),(1)]=

(ii) [∀∃∀,(0,1),(1)]

(iii) [∀∃,(0),(1)]=

http://logic.rwth-aachen.de/Teaching/AMT-WS12/

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