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

Published online by Cambridge University Press:  12 March 2014

Andrea Cantini
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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/abstractionon 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 2 , June 1993 , pp. 477 - 513
Copyright
Copyright © Association for Symbolic Logic 1993

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