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  1. Classical Recursion Theory. The Theory of Functions and Sets of Natural Numbers.Peter G. Hinman - 1990 - Journal of Symbolic Logic 55 (3):1307-1308.
  • A Revenge-Immune Solution to the Semantic Paradoxes.Hartry Field - 2003 - Journal of Philosophical Logic 32 (2):139-177.
    The paper offers a solution to the semantic paradoxes, one in which we keep the unrestricted truth schema “True↔A”, and the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True with A within the (...)
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  • The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
  • Games for Truth.P. D. Welch - 2009 - Bulletin of Symbolic Logic 15 (4):410-427.
    We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.
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  • Naive Semantics and the Liar Paradox.Hans G. Herzberger - 1982 - Journal of Philosophy 79 (9):479-497.
  • Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
    A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.
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  • The Revision Theory of Truth.Vann McGee - 1996 - Philosophy and Phenomenological Research 56 (3):727-730.
  • Notes on Naive Semantics.Hans G. Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
  • The Truth is Never Simple.John P. Burgess - 1986 - Journal of Symbolic Logic 51 (3):663-681.
    The complexity of the set of truths of arithmetic is determined for various theories of truth deriving from Kripke and from Gupta and Herzberger.
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  • Truth, Logical Validity and Determinateness: A Commentary on Field’s Saving Truth From Paradox.P. D. Welch - 2011 - Review of Symbolic Logic 4 (3):348-359.
    We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path-dependent hierarchies of his determinateness operator.
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  • Comments on Martin’s and Welch’s Comments.Hartry Field - 2011 - Review of Symbolic Logic 4 (3):360-366.
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  • Field’s Saving Truth From Paradox: Some Things It Doesn’T Do.Donald A. Martin - 2011 - Review of Symbolic Logic 4 (3):339-347.
    I will discuss Fields Outline of a Theory of Truth. I will point out important properties of Kripkeleast fixed points constructions and theory. I do this not to demean Field’s superb work on truth but rather to suggest that there may be no really satisfactory conditional connective for languages containing their own truth predicates.
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  • Revision Revisited.Leon Horsten, Graham E. Leigh, Hannes Leitgeb & Philip Welch - 2012 - Review of Symbolic Logic 5 (4):642-664.
    This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.
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  • Ultimate Truth Vis- À- Vis Stable Truth.P. D. Welch - 2008 - Review of Symbolic Logic 1 (1):126-142.
    We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (...)
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  • On the Semantics of the Constructible Levels.George Boolos - 1970 - Mathematical Logic Quarterly 16 (2):139-148.
  • Revision and its Rivals.Donald A. Martin - 1997 - Philosophical Issues 8:407-418.