Annals of Pure and Applied Logic 163 (11):1484-1523 (2012)

Authors
Kentaro Fujimoto
University of Bristol
Abstract
This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of the reflection principle, are also presented. The equivalence results among systems of truth and classes obtained in this article are summarized in Theorem 104 , Theorem 107 and Theorem 108
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DOI 10.1016/j.apal.2011.12.006
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References found in this work BETA

The Concept of Truth in Formalized Languages.Alfred Tarski - 1936 - In A. Tarski (ed.), Logic, Semantics, Metamathematics. Oxford University Press. pp. 152--278.
Reflecting on Incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
Transfinite Recursive Progressions of Axiomatic Theories.Solomon Feferman - 1962 - Journal of Symbolic Logic 27 (3):259-316.
How Truthlike Can a Predicate Be? A Negative Result.Vann McGee - 1985 - Journal of Philosophical Logic 14 (4):399 - 410.
Relative Truth Definability of Axiomatic Truth Theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.

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Citations of this work BETA

Axiomatic Theories of Truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.
Arithmetical Reflection and the Provability of Soundness.Walter Dean - 2015 - Philosophia Mathematica 23 (1):31-64.
Universism and Extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - forthcoming - Review of Symbolic Logic:1-50.

View all 23 citations / Add more citations

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