Kreisel's Conjecture with minimality principle
Pavel Hrubeš
Source: J. Symbolic Logic
Volume 74, Issue 3
(2009), 976-988.
Abstract
We prove that Kreisel's Conjecture is true, if Peano arithmetic is
axiomatised using minimality principle and axioms of identity (theory
PAM). The result is independent on the choice of language of
PAM. We also show that if infinitely many instances of A(x) are
provable in a bounded number of steps in PAM then there exists
k∈ω s.t. PAM⊢ ∀ x > \overline{k} A(x). The results imply that PAM does not prove scheme of induction or identity schemes in a bounded number of steps.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1245158094
Digital Object Identifier: doi:10.2178/jsl/1245158094
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