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2008 Tennenbaum's Theorem and Unary Functions
Sakae Yaegasi
Notre Dame J. Formal Logic 49(2): 177-183 (2008). DOI: 10.1215/00294527-2008-006

Abstract

It is well known that in any nonstandard model of PA (Peano arithmetic) neither addition nor multiplication is recursive. In this paper we focus on the recursiveness of unary functions and find several pairs of unary functions which cannot be both recursive in the same nonstandard model of PA (e.g., 2x , 2x + 1 , x 2 , 2 x 2 , and 2 x 3 x ). Furthermore, we prove that for any computable injection f x , there is a nonstandard model of PA in which f x is recursive.

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Sakae Yaegasi. "Tennenbaum's Theorem and Unary Functions." Notre Dame J. Formal Logic 49 (2) 177 - 183, 2008. https://doi.org/10.1215/00294527-2008-006

Information

Published: 2008
First available in Project Euclid: 15 May 2008

zbMATH: 1143.03037
MathSciNet: MR2402040
Digital Object Identifier: 10.1215/00294527-2008-006

Subjects:
Primary: 03H15
Secondary: 03C62 , 03F30

Keywords: nonstandard models , Peano Arithmetic , Tennenbaum's theorem

Rights: Copyright © 2008 University of Notre Dame

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Vol.49 • No. 2 • 2008
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