From proof theory to theories theory

Abstract

In the last decades, several objects such as grammars, economical agents, laws of physics... have been defined as algorithms. In particular, after Brouwer, Heyting, and Kolomogorov, mathematical proofs have been defined as algorithms. In this paper, we show that mathematical theories can be also be defined as algorithms and that this definition has some advantages over the usual definition of theories as sets of axioms.