Abstract
Publisher Summary This chapter describes Friedman's contributions to intuitionistic set theory. These contributions include Friedman's extension of Gael's negative interpretation and Friedman's extension of Kleene's recursive realizability. One of the first significant results about intuitionistic systems was obtained in 1932 by Godel who gave a syntactical translation of classical predicate calculus into Heyting's predicate calculus. Thus the consistency of a system with classical logic is reduced to the consistency of a system with intuitionistic logic, and furthermore the classical system can be viewed as a subsystem (or a special case) of an intuitionistic one. Finally, the chapter discusses the partially intuitionistic fragments of ZFC for which Excluded Middle holds for an important class of formulas.
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