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Kreisel's Conjecture with minimality principle

Published online by Cambridge University Press:  12 March 2014

Pavel Hrubeš
Pavel Hrubeš*
Affiliation:
Institute for Advanced Study, Einstein Drive, Princeton, Nj 08540, USA, E-mail: pahrubes@centrum.cz
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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 . The results imply that PAM does not prove scheme of induction or identity schemes in a bounded number of steps.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 976 - 988
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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