Extending the First-Order Theory of Combinators with Self-Referential Truth
Andrea Cantini
Source: J. Symbolic Logic Volume 58, Issue 2
(1993), 477-513.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1183744244
JSTOR: links.jstor.org
Mathematical Reviews number (MathSciNet): MR1233921
Zentralblatt MATH identifier: 0795.03075
