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

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

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.

Categories

Keywords

Reprint years

DOI

10.2307/2275216

Other Versions

No versions found

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Levels of Truth.Andrea Cantini - 1995 - Notre Dame Journal of Formal Logic 36 (2):185-213.
Higher-Order Logic and Disquotational Truth.Lavinia Picollo & Thomas Schindler - 2022 - Journal of Philosophical Logic 51 (4):879-918.
Systems of illative combinatory logic complete for first-order propositional and predicate calculus.Henk Barendregt, Martin Bunder & Wil Dekkers - 1993 - Journal of Symbolic Logic 58 (3):769-788.
First-Order Logic and First-Order Functions.Rodrigo A. Freire - 2015 - Logica Universalis 9 (3):281-329.
Interpreting the compositional truth predicate in models of arithmetic.Cezary Cieśliński - 2021 - Archive for Mathematical Logic 60 (6):749-770.
First-Order Predicate Logics.Petr Cintula & Carles Noguera - 2021 - In Petr Cintula & Carles Noguera, Logic and Implication: An Introduction to the General Algebraic Study of Non-classical Logics. Cham: Springer Verlag. pp. 347-412.
A beginner's further guide to mathematical logic.Raymond M. Smullyan - 2017 - New Jersey: World Scientific.
A Note on Typed Truth and Consistency Assertions.Carlo Nicolai - 2016 - Journal of Philosophical Logic 45 (1):89-119.
S. Feferman. Reflecting on incompleteness. The Journal of Symbolic Logic, vol. 56 , no. 1, pp. 1–49. - W. N. Reinhardt. Some remarks on extending and interpreting theories with a partial predicate for truth. Journal of Philosophical Logic, vol. 15 , no. 2, pp. 219–251. - V. Halbach and L. Horsten. Axiomatizing Kripke’s theory of truth. The Journal of Symbolic Logic, vol. 71 , no. 2, pp. 667–712 - H. Friedman and M. Sheard. An axiomatic approach to self-referential truth.Annals of Pure and Applied Logic, vol. 33 , no. 1, pp. 1–21. - V. Halbach. A system of complete and consistent truth. Notre Dame Journal of Formal Logic, vol. 35 , no. 3, pp. 311–327.Graham E. Leigh - 2010 - Bulletin of Symbolic Logic 16 (3):424-428.
The abstract variable-binding calculus.Don Pigozzi & Antonino Salibra - 1995 - Studia Logica 55 (1):129 - 179.

Analytics

Added to PP
2009-01-28

Downloads
167 (#246,698)

6 months
43 (#197,025)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Photo of Andrea Cantini
Andrea Cantini
Università degli Studi di Firenze

Citations of this work

Axiomatische Wahrheitstheorien.Volker Halbach - 1996 - Berlin, Boston: De Gruyter.
Truth in applicative theories.Reinhard Kahle - 2001 - Studia Logica 68 (1):103-128.
Universes over Frege structures.Reinhard Kahle - 2003 - Annals of Pure and Applied Logic 119 (1-3):191-223.
Theories of Frege structure equivalent to Feferman's system T 0.Daichi Hayashi - 2025 - Annals of Pure and Applied Logic 176 (1):103510.
The universal set and diagonalization in Frege structures.Reinhard Kahle - 2011 - Review of Symbolic Logic 4 (2):205-218.

View all 6 citations / Add more citations

References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
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.

View all 15 references / Add more references