Notre Dame Journal of Formal Logic

The Arithmetics of a Theory

Albert Visser

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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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Notre Dame J. Formal Logic Volume 56, Number 1 (2015), 81-119.

First available in Project Euclid: 24 March 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F45: Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]
Secondary: 03F30: First-order arithmetic and fragments 03F40: Gödel numberings and issues of incompleteness 03F25: Relative consistency and interpretations

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


Visser, Albert. The Arithmetics of a Theory. Notre Dame J. Formal Logic 56 (2015), no. 1, 81--119. doi:10.1215/00294527-2835029.

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