## Notre Dame Journal of Formal Logic

### The Arithmetics of a Theory

Albert Visser

#### Abstract

In this paper we study the interpretations of a weak arithmetic, like Buss’s theory $\mathsf{S}^{1}_{2}$, 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.

#### Article information

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

Dates
First available in Project Euclid: 24 March 2015

https://projecteuclid.org/euclid.ndjfl/1427202975

Digital Object Identifier
doi:10.1215/00294527-2835029

Mathematical Reviews number (MathSciNet)
MR3326590

Zentralblatt MATH identifier
1350.03045

#### Citation

Visser, Albert. The Arithmetics of a Theory. Notre Dame J. Formal Logic 56 (2015), no. 1, 81--119. doi:10.1215/00294527-2835029. https://projecteuclid.org/euclid.ndjfl/1427202975

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