In this paper we study the interpretations of a weak arithmetic, like Buss’s theory , in a given theory . We call these interpretations the arithmetics of . We develop the basics of the structure of the arithmetics of . We study the provability logic(s) of from the standpoint of the framework of the arithmetics of . Finally, we provide a deeper study of the arithmetics of a finitely axiomatized sequential theory.
"The Arithmetics of a Theory." Notre Dame J. Formal Logic 56 (1) 81 - 119, 2015. https://doi.org/10.1215/00294527-2835029