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

Journal of Symbolic Logic 58 (2):477-513 (1993)
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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

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2009-01-28

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Andrea Cantini
Università degli Studi di Firenze

Citations of this work

Universes over Frege structures.Reinhard Kahle - 2003 - Annals of Pure and Applied Logic 119 (1-3):191-223.
The universal set and diagonalization in Frege structures.Reinhard Kahle - 2011 - Review of Symbolic Logic 4 (2):205-218.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The Lambda Calculus. Its Syntax and Semantics.E. Engeler - 1984 - Journal of Symbolic Logic 49 (1):301-303.
Theory of Formal Systems.Raymond M. Smullyan - 1965 - Journal of Symbolic Logic 30 (1):88-90.
Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Zeitshrift für Mathematische Logik Und Grundlagen der Mathematik 35 (1):97--130.
Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Mathematical Logic Quarterly 35 (2):97-130.

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