Abstract

In his 1946 Princeton Bicentennial Lecture Gödel suggested the problem of transferring the Turing analysis of computability to definability and provability, in particular of finding a notion of definability which is "formalism free" in a sense similar to the notion of computable function --- a notion which is very robust with respect to its various associated formalisms. One way to interpret this suggestion is to consider standard notions of definability, which are usually built over first order logic, and change the underlying logic. We observe that under an extensional notion of meaning for set theoretic discourse, Quine's Dictum "change of logic implies change of meaning" is only partially true. This is joint work with Menachem Magidor and Jouko Väänänen.