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Theories very close to PA where Kreisel's Conjecture is false

Published online by Cambridge University Press:  12 March 2014

Pavel Hrubeš
Pavel Hrubeš*
Affiliation:
Mathematical Institute, Academy of Sciences of the Czech Republic, Prague, Czech Republic. E-mail: pahrubes@centrum.cz
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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 L 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 123 - 137
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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