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

Journal of Symbolic Logic 58 (2):477-513 (1993)
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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DOI 10.2307/2275216
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Reinhard Kahle (2003). Universes Over Frege Structures. Annals of Pure and Applied Logic 119 (1-3):191-223.

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