, Volume 53, Issue 1-2, pp 27-61

On The Logic Of Reducibility: Axioms And Examples

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Abstract

This paper is an investigation into what could be a goodexplication of ``theory S is reducible to theory T''. Ipresent an axiomatic approach to reducibility, which is developedmetamathematically and used to evaluate most of the definitionsof ``reducible'' found in the relevant literature. Among these,relative interpretability turns out to be most convincing as ageneral reducibility concept, proof-theoreticalreducibility being its only serious competitor left. Thisrelation is analyzed in some detail, both from the point of viewof the reducibility axioms and of modal logic.