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2015 The Arithmetics of a Theory
Albert Visser
Notre Dame J. Formal Logic 56(1): 81-119 (2015). DOI: 10.1215/00294527-2835029

Abstract

In this paper we study the interpretations of a weak arithmetic, like Buss’s theory S21, in a given theory U. We call these interpretations the arithmetics of U. We develop the basics of the structure of the arithmetics of U. We study the provability logic(s) of U from the standpoint of the framework of the arithmetics of U. Finally, we provide a deeper study of the arithmetics of a finitely axiomatized sequential theory.

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Albert Visser. "The Arithmetics of a Theory." Notre Dame J. Formal Logic 56 (1) 81 - 119, 2015. https://doi.org/10.1215/00294527-2835029

Information

Published: 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1350.03045
MathSciNet: MR3326590
Digital Object Identifier: 10.1215/00294527-2835029

Subjects:
Primary: 03F45
Secondary: 03F25 , 03F30 , 03F40

Keywords: $\Sigma_{1}$-sentence , interpretation , provability logic , weak arithmetic

Rights: Copyright © 2015 University of Notre Dame

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Vol.56 • No. 1 • 2015
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