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Kentaro Sato (2011). The Strength of Extensionality II—Weak Weak Set Theories Without Infinity.

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  1.  12
    A New Model Construction by Making a Detour Via Intuitionistic Theories I: Operational Set Theory Without Choice is Π 1 -Equivalent to KP.Kentaro Sato & Rico Zumbrunnen - 2015 - Annals of Pure and Applied Logic 166 (2):121-186.
  2.  34
    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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    Admissible Closures of Polynomial Time Computable Arithmetic.Dieter Probst & Thomas Strahm - 2011 - Archive for Mathematical Logic 50 (5-6):643-660.
    We propose two admissible closures ${\mathbb{A}({\sf PTCA})}$ and ${\mathbb{A}({\sf PHCA})}$ of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i) ${\mathbb{A}({\sf PTCA})}$ is conservative over PTCA with respect to ${\forall\exists\Sigma^b_1}$ sentences, and (ii) ${\mathbb{A}({\sf PHCA})}$ is conservative over full bounded arithmetic PHCA for ${\forall\exists\Sigma^b_{\infty}}$ sentences. This yields that (i) the ${\Sigma^b_1}$ definable functions of ${\mathbb{A}({\sf PTCA})}$ are the polytime functions, and (ii) the ${\Sigma^b_{\infty}}$ definable (...)
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