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2012 Weak Theories of Concatenation and Arithmetic
Yoshihiro Horihata
Notre Dame J. Formal Logic 53(2): 203-222 (2012). DOI: 10.1215/00294527-1715698

Abstract

We define a new theory of concatenation WTC which is much weaker than Grzegorczyk's well-known theory TC. We prove that WTC is mutually interpretable with the weak theory of arithmetic R. The latter is, in a technical sense, much weaker than Robinson's arithmetic Q, but still essentially undecidable. Hence, as a corollary, WTC is also essentially undecidable.

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Yoshihiro Horihata. "Weak Theories of Concatenation and Arithmetic." Notre Dame J. Formal Logic 53 (2) 203 - 222, 2012. https://doi.org/10.1215/00294527-1715698

Information

Published: 2012
First available in Project Euclid: 9 May 2012

zbMATH: 1251.03075
MathSciNet: MR2925278
Digital Object Identifier: 10.1215/00294527-1715698

Subjects:
Primary: 03F25

Keywords: interpretation , Robinson's arithmetic , theory of concatenation

Rights: Copyright © 2012 University of Notre Dame

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Vol.53 • No. 2 • 2012
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