The arithmetics of a theory
Publication date
2015
Authors
Visser, Albert
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Document Type
Article
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taverne
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.
Keywords
interpretation, weak arithmetic, provability logic, Sigma_1-sentence, Taverne, General Mathematics, General Arts and Humanities
Citation
Visser, A 2015, 'The arithmetics of a theory', Notre Dame Journal of Formal Logic, vol. 56, no. 1, pp. 81-119. https://doi.org/10.1215/00294527-2835029