On the logic of reducibility: Axioms and examples

Abstract

This paper is an investigation into what could be a good explication of "theory S is reducible to theory T". I present an axiomatic approach to reducibility, which is developed metamathematically and used to evaluate most of the definitions of "reducible" found in the relevant literature. Among these, relative interpretability turns out to be most convincing as a general reducibility concept, proof-theoretical reducibility being its only serious competitor left. This relation is analyzed in some detail, both from the point of view of the reducibility axioms and of modal logic. © 2000 Kluwer Academic Publishers.