Set Theoretic Foundations for Constructive Analysis
Harvey Friedman · Annals of Mathematics · 1977
We introduce an extensional set theoretic formalism B, a subsystem of Zermelo set theory based on intuitionistic logic, which provides a set theoretic foundation for constructive analysis which is strikingly analogous to the usual set theoretic foundations for ordinary analysis. We prove that B has the same elementary (LL?) consequences as first order arithmetic, and that every arithmetic consequence of B is a consequence of Peano arithmetic. We indicate a definitional translation of B into an intensional theory of predicates, which in turn has a natural interpretation in the informal theory