Abstract
This chapter presents an abstract notion of realizabillty for which intuitionistic predicate calculus is complete. It is shown that A is derivable in Heyting's predicate calculus if there is an explicitly definable functional Θ such that Θ ɛ p [ A ] for all p , that is, if there is a well defined proof of A that does not make use of the internal structure of proofs of the atomic parts of A . The chapter makes the use of the analogy between Kripke's semantics for intuitionistic logic and the theory of permutation groups. The corresponding result for propositional logic was announced in an abstract.
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