The Arithmetics of a Theory
Copyright policy )The Arithmetics of a Theory
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.
- Utrecht University Netherlands
General Mathematics, General Arts and Humanities, weak arithmetic, Sigma_1-sentence, $\Sigma_{1}$-sentence, 03F45, Wijsbegeerte, Taverne, 03F25, provability logic, 03F40, 03F30, interpretation
General Mathematics, General Arts and Humanities, weak arithmetic, Sigma_1-sentence, $\Sigma_{1}$-sentence, 03F45, Wijsbegeerte, Taverne, 03F25, provability logic, 03F40, 03F30, interpretation
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