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  1.  9
    Dependent Choices and Anti-Foundation.Hisato Muraki - 2002 - Mathematical Logic Quarterly 48 (4):607-623.
    In Zermelo-Fraenkel set theory without the Axiom of Foundation we study the schema version of the principle of dependent choices in connection with Aczel's antifoundation axiom , Boffa's anti-foundation axiom, and axiom of collection.
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  2.  13
    Non‐Complementedness and Non‐Distributivity of Kleene Degrees.Hisato Muraki - 1997 - Mathematical Logic Quarterly 43 (3):378-388.
    In this note, we study the complementedness and the distributivity of upper semilattices of Kleene degrees assuming V = L. K denotes the upper semilattice of all Kleene degrees. We prove that if V = L, then some sub upper semilattices of K are non-complemented and some are non-distributive.
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  3.  11
    Local Density of Kleene Degrees.Hisato Muraki - 1995 - Mathematical Logic Quarterly 41 (2):183-189.
    Concerning Post's problem for Kleene degrees and its relativization, Hrbacek showed in [1] and [2] that if V = L, then Kleene degrees of coanalytic sets are dense, and then for all K ⊆ωω, there are N1 sets which are Kleene semirecursive in K and not Kleene recursive in each other and K. But the density of Kleene semirecursive in K Kleene degrees is not obtained from these theorems. In this note, we extend these theorems by showing that if V (...)
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  4.  11
    Largest Fixed Points of Set Continuous Operators and Boffa's Anti-Foundation.Hisato Muraki - 2005 - Mathematical Logic Quarterly 51 (4):365.
    In Aczel [1], the existence of largest fixed points of set continuous operators is proved assuming the schema version of dependent choices in Zermelo-Fraenkel set theory without the axiom of Foundation. In the present paper, we study whether the existence of largest fixed points of set continuous operators is provable without the schema version of dependent choices, using Boffa's weak antifoundation axioms.
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