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67Arithmetical Sacks ForcingArchive for Mathematical Logic 45 (6): 715-720. 2006.We answer a question of Jockusch by constructing a hyperimmune-free minimal degree below a 1-generic one. To do this we introduce a new forcing notion called arithmetical Sacks forcing. Some other applications are presented.
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112Maximal pairs of c.e. reals in the computably Lipschitz degreesAnnals of Pure and Applied Logic 162 (5): 357-366. 2011.Computably Lipschitz reducibility , was suggested as a measure of relative randomness. We say α≤clβ if α is Turing reducible to β with oracle use on x bounded by x+c. In this paper, we prove that for any non-computable real, there exists a c.e. real so that no c.e. real can cl-compute both of them. So every non-computable c.e. real is the half of a cl-maximal pair of c.e. reals
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88Characterizing strong randomness via Martin-Löf randomnessAnnals of Pure and Applied Logic 163 (3): 214-224. 2012.
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29Zheng ju xiang guan xing yan jiu =Beijing da xue chu ban she. 2008.本书从界定证据相关性的内涵入手,分别探讨了逻辑上的相关性和法律上的相关性,从而澄清了一些在借鉴英美国家证据规则时出现的概念混淆。
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113A new proof of Friedman's conjectureBulletin of Symbolic Logic 17 (3): 455-461. 2011.We give a new proof of Friedman's conjecture that every uncountable Δ11 set of reals has a member of each hyperdegree greater than or equal to the hyperjump
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94Maximal Chains in the Turing DegreesJournal of Symbolic Logic 72 (4): 1219-1227. 2007.We study the problem of existence of maximal chains in the Turing degrees. We show that: 1. ZF+DC+"There exists no maximal chain in the Turing degrees" is equiconsistent with ZFC+"There exists an inaccessible cardinal"; 2. For all a ∈ 2ω.(ω₁)L[a] = ω₁ if and only if there exists a $\Pi _{1}^{1}[a]$ maximal chain in the Turing degrees. As a corollary, ZFC + "There exists an inaccessible cardinal" is equiconsistent with ZFC + "There is no (bold face) $\utilde{\Pi}{}_{1}^{1}$ maximal chain of Turin…Read more
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74Measure Theory Aspects of Locally Countable OrderingsJournal of Symbolic Logic 71 (3). 2006.We prove that for any locally countable $\Sigma _{1}^{1}$ partial order P = 〈2ω,≤P〉, there exists a nonmeasurable antichain in P. Some applications of the result are also presented
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235Lowness and Π₂⁰ nullsetsJournal of Symbolic Logic 71 (3): 1044-1052. 2006.We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness
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120On Σ₁-Structural Differences among Finite Levels of the Ershov HierarchyJournal of Symbolic Logic 71 (4). 2006.We show that the structure R of recursively enumerable degrees is not a Σ₁-elementary substructure of Dn, where Dn (n &gt 1) is the structure of n-r.e. degrees in the Ershov hierarchy
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151On the Definable Ideal Generated by Nonbounding C.E. DegreesJournal of Symbolic Logic 70 (1). 2005.Let [NB]₁ denote the ideal generated by nonbounding c.e. degrees and NCup the ideal of noncuppable c.e. degrees. We show that both [NB]₁ ∪ NCup and the ideal generated by nonbounding and noncuppable degrees are new, in the sense that they are different from M, [NB]₁ and NCup—the only three known definable ideals so far
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108There Is No SW-Complete C.E. RealJournal of Symbolic Logic 69 (4). 2004.We prove that there is no sw-complete c.e. real, negatively answering a question in [6]
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101There Are No Maximal Low D.C.E. DegreesNotre Dame Journal of Formal Logic 45 (3): 147-159. 2004.We prove that there is no maximal low d.c.e degree
