Extending the first-order theory of combinators with self-referential truth

Publisher: Cambridge University Press

E-ISSN: 1943-5886|58|2|477-513

ISSN: 0022-4812

Source: The Journal of Symbolic Logic, Vol.58, Iss.2, 1993-06, pp. : 477-513

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Abstract

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.