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March 2007 Theories very close to PA where Kreisel's Conjecture is false
Pavel Hrubeš
J. Symbolic Logic 72(1): 123-137 (March 2007). DOI: 10.2178/jsl/1174668388

Abstract

We give four examples of theories in which Kreisel's Conjecture is false: (1) the theory PA(-) obtained by adding a function symbol minus, ‘-’, to the language of PA, and the axiom ∀ x∀ y ∀ z (x-y=z) ≡ (x=y+z ∨ (x < y ∧ z=0)); (2) the theory 𝒵 of integers; (3) the theory PA(q) obtained by adding a function symbol q (of arity ≥ 1) to PA, assuming nothing about q; (4) the theory PA(N) containing a unary predicate N(x) meaning ‘x is a natural number’. In Section 6 we suggest a counterexample to the so called Sharpened Kreisel's Conjecture.

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Pavel Hrubeš. "Theories very close to PA where Kreisel's Conjecture is false." J. Symbolic Logic 72 (1) 123 - 137, March 2007. https://doi.org/10.2178/jsl/1174668388

Information

Published: March 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1117.03065
MathSciNet: MR2298475
Digital Object Identifier: 10.2178/jsl/1174668388

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 1 • March 2007
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