Journal of Symbolic Logic

Extending the First-Order Theory of Combinators with Self-Referential Truth

Andrea Cantini

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The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursion theory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.

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J. Symbolic Logic Volume 58, Issue 2 (1993), 477-513.

First available in Project Euclid: 6 July 2007

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Cantini, Andrea. Extending the First-Order Theory of Combinators with Self-Referential Truth. J. Symbolic Logic 58 (1993), no. 2, 477--513.

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