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  1.  55
    Classes and Truths in Set Theory.Kentaro Fujimoto - 2012 - Annals of Pure and Applied Logic 163 (11):1484-1523.
    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, (...)
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  2. Relative Truth Definability of Axiomatic Truth Theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.
    The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].
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  3.  35
    Predicativism About Classes.Kentaro Fujimoto - 2019 - Journal of Philosophy 116 (4):206-229.
    Classes are the objects of the second sort of second-order set theory. They have sets as their members and behave like sets, but paradoxes tell us that many classes cannot be sets. Then, what are classes? Predicativism about classes suggests that classes are predicates of sets, and this article investigates the question from the predicativist point of view in light of recent developments in the use of classes in set theory. Predicativism has been considered too restrictive and unable to accommodate (...)
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  4.  30
    Deflationism Beyond Arithmetic.Kentaro Fujimoto - 2019 - Synthese 196 (3):1045-1069.
    The conservativeness argument poses a dilemma to deflationism about truth, according to which a deflationist theory of truth must be conservative but no adequate theory of truth is conservative. The debate on the conservativeness argument has so far been framed in a specific formal setting, where theories of truth are formulated over arithmetical base theories. I will argue that the appropriate formal setting for evaluating the conservativeness argument is provided not by theories of truth over arithmetic but by those over (...)
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  5.  33
    Autonomous Progression and Transfinite Iteration of Self-Applicable Truth.Kentaro Fujimoto - 2011 - Journal of Symbolic Logic 76 (3):914 - 945.
    This paper studies several systems of the transfinite iteration and autonomous progression of self-applicable truth and determines their proof-theoretic strength.
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  6.  37
    Notes on Some Second-Order Systems of Iterated Inductive Definitions and Π 1 1 -Comprehensions and Relevant Subsystems of Set Theory. [REVIEW]Kentaro Fujimoto - 2015 - Annals of Pure and Applied Logic 166 (4):409-463.
  7.  14
    Truths, Inductive Definitions, and Kripke-Platek Systems Over Set Theory.Kentaro Fujimoto - 2018 - Journal of Symbolic Logic 83 (3):868-898.
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  8. Introduction.José Martínez-Fernández, Henri Galinon, Kentaro Fujimoto & Theodora Achourioti - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag.
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