The arithmetics of a theory

A. Visser

doi:10.1215/00294527-2835029

The arithmetics of a theory

A. Visser

OFR - Theoretical Philosophy

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In this paper we study the interpretations of a weak arithmetic, like Buss' theory S^1_2, 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.

Original language	English
Pages (from-to)	81-119
Number of pages	39
Journal	Notre Dame Journal of Formal Logic
Volume	56
Issue number	1
DOIs	https://doi.org/10.1215/00294527-2835029
Publication status	Published - 2015

Keywords

interpretation
weak arithmetic
provability logic
Sigma_1-sentence

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10.1215/00294527-2835029

euclid.ndjfl.1427202975Final published version, 624 KBLicence: Taverne

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AB - In this paper we study the interpretations of a weak arithmetic, like Buss' theory S^1_2, 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.

KW - interpretation

KW - weak arithmetic

KW - provability logic

KW - Sigma_1-sentence

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DO - 10.1215/00294527-2835029

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JO - Notre Dame Journal of Formal Logic

JF - Notre Dame Journal of Formal Logic

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The arithmetics of a theory

Abstract

Keywords

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