7 found
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  1.  43
    Uniform versions of some axioms of second order arithmetic.Nobuyuki Sakamoto & Takeshi Yamazaki - 2004 - Mathematical Logic Quarterly 50 (6):587-593.
    In this paper, we discuss uniform versions of some axioms of second order arithmetic in the context of higher order arithmetic. We prove that uniform versions of weak weak König's lemma WWKL and Σ01 separation are equivalent to over a suitable base theory of higher order arithmetic, where is the assertion that there exists Φ2 such that Φf1 = 0 if and only if ∃x0 for all f. We also prove that uniform versions of some well-known theorems are equivalent to (...)
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  2.  56
    Some conservation results on weak König's lemma.Stephen G. Simpson, Kazuyuki Tanaka & Takeshi Yamazaki - 2002 - Annals of Pure and Applied Logic 118 (1-2):87-114.
    By , we denote the system of second-order arithmetic based on recursive comprehension axioms and Σ10 induction. is defined to be plus weak König's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. In this paper, we first show that for any countable model M of , there exists a countable model M′ of whose first-order part is the same as that of M, and whose second-order part consists of the M-recursive sets and sets not (...)
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  3.  63
    A non-standard construction of Haar measure and weak könig's lemma.Kazuyuki Tanaka & Takeshi Yamazaki - 2000 - Journal of Symbolic Logic 65 (1):173-186.
    In this paper, we show within RCA 0 that weak Konig's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within WKL 0 , a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of WKL 0 has a proper initial part isomorphic to itself [10].
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  4.  15
    Some More Conservation Results on the Baire Category Theorem.Takeshi Yamazaki - 2000 - Mathematical Logic Quarterly 46 (1):105-110.
    In this paper, we generalize a result of Brown and Simpson [1] to prove that RCA0+Π0∞-BCT is conservative over RCA0 with respect to the set of formulae in the form ∃!Xφ, where φ is arithmetical. We also consider the conservation of Π00∞-BCT over Σb1-NIA+∇b1-CA.
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  5.  32
    Does truth-table of linear norm reduce the one-query tautologies to a random oracle?Masahiro Kumabe, Toshio Suzuki & Takeshi Yamazaki - 2008 - Archive for Mathematical Logic 47 (2):159-180.
    In our former works, for a given concept of reduction, we study the following hypothesis: “For a random oracle A, with probability one, the degree of the one-query tautologies with respect to A is strictly higher than the degree of A.” In our former works (Suzuki in Kobe J. Math. 15, 91–102, 1998; in Inf. Comput. 176, 66–87, 2002; in Arch. Math. Logic 44, 751–762), the following three results are shown: The hypothesis for p-T (polynomial-time Turing) reduction is equivalent to (...)
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  6.  41
    Two kinds of fixed point theorems and reverse mathematics.Weiguang Peng & Takeshi Yamazaki - 2017 - Mathematical Logic Quarterly 63 (5):454-461.
    In this paper, we investigate the logical strength of two types of fixed point theorems in the context of reverse mathematics. One is concerned with extensions of the Banach contraction principle. Among theorems in this type, we mainly show that the Caristi fixed point theorem is equivalent to math formula over math formula. The other is dedicated to topological fixed point theorems such as the Brouwer fixed point theorem. We introduce some variants of the Fan-Browder fixed point theorem and the (...)
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  7.  59
    Reverse Mathematics and Completeness Theorems for Intuitionistic Logic.Takeshi Yamazaki - 2001 - Notre Dame Journal of Formal Logic 42 (3):143-148.
    In this paper, we investigate the logical strength of completeness theorems for intuitionistic logic along the program of reverse mathematics. Among others we show that is equivalent over to the strong completeness theorem for intuitionistic logic: any countable theory of intuitionistic predicate logic can be characterized by a single Kripke model.
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