Classes and truths in set theory

Annals of Pure and Applied Logic 163 (11):1484-1523 (2012)
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
Relative Truth Definability of Axiomatic Truth Theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.
Reflecting on Incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
An Axiomatic Approach to Self-Referential Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 33 (1):1--21.
Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Zeitshrift für Mathematische Logik Und Grundlagen der Mathematik 35 (1):97--130.
The Concept of Truth in Formalized Languages.Alfred Tarski - 1936 - In A. Tarski (ed.), Logic, Semantics, Metamathematics. Oxford University Press. pp. 152--278.

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Citations of this work BETA
A Note on Typed Truth and Consistency Assertions.Carlo Nicolai - 2016 - Journal of Philosophical Logic 45 (1):89-119.
The Expressive Power of Truth.Martin Fischer & Leon Horsten - 2015 - Review of Symbolic Logic 8 (2):345-369.
The Groundedness Approach to Class Theory.Jönne Kriener - 2014 - Inquiry : An Interdisciplinary Journal of Philosophy 57 (2):244-273.

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