Journal of Symbolic Logic

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

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/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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

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

Citation

Cantini, Andrea. Extending the First-Order Theory of Combinators with Self-Referential Truth. Journal of Symbolic Logic 58 (1993), no. 2, 477--513. http://projecteuclid.org/euclid.jsl/1183744244.


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