25 found
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  1.  29
    Computability, Enumerability, Unsolvability, Directions in Recursion Theory, Edited by S. B. Cooper, T. A. Slaman, and S. S. Wainer, London Mathematical Society Lecture Note Series, No. 224, Cambridge University Press, Cambridge, New York, and Oakleigh, Victoria, 1996, Vii + 347 Pp. - Leo Harrington and Robert I. Soare, Dynamic Properties of Computably Enumerable Sets, Pp. 105–121. - Eberhard Herrmann, On the ∀∃-Theory of the Factor Lattice by the Major Subset Relation, Pp. 139–166. - Manuel Lerman, Embeddings Into the Recursively Enumerable Degrees, Pp. 185–204. - Xiaoding Yi, Extension of Embeddings on the Recursively Enumerable Degrees Modulo the Cappable Degrees, Pp. 313–331. - André Nies, Relativization of Structures Arising From Computability Theory. Pp. 219–232. - Klaus Ambos-Spies, Resource-Bounded Genericity. Pp. 1–59. - Rod Downey, Carl G. Jockusch, and Michael Stob. Array Nonrecursive Degrees and Genericity, Pp. 93–104. - Masahiro Kumabe, Degrees of Generic Sets, Pp. 167–183. [REVIEW]C. T. Chong - 1999 - Journal of Symbolic Logic 64 (3):1362-1365.
  2.  5
    Randomness in the Higher Setting.C. T. Chong & Liang Yu - 2015 - Journal of Symbolic Logic 80 (4):1131-1148.
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  3.  7
    Nonstandard Models in Recursion Theory and Reverse Mathematics.C. T. Chong, Wei Li & Yue Yang - 2014 - Bulletin of Symbolic Logic 20 (2):170-200.
  4.  23
    Minimal Degrees Recursive in 1-Generic Degrees.C. T. Chong & R. G. Downey - 1990 - Annals of Pure and Applied Logic 48 (3):215-225.
  5.  9
    ∑2 Induction and Infinite Injury Priority Arguments, Part II Tame ∑2 Coding and the Jump Operator.C. T. Chong & Yue Yang - 1997 - Annals of Pure and Applied Logic 87 (2):103-116.
  6.  34
    ∑1‐Density and Turing Degrees.C. T. Chong - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (2):141-145.
  7.  4
    Hyperhypersimple α-r.e. sets.C. T. Chong & M. Lerman - 1976 - Annals of Mathematical Logic 9 (1-2):1-48.
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  8.  28
    Σ2 Induction and Infinite Injury Priority Argument, Part I: Maximal Sets and the Jump Operator.C. T. Chong & Yue Yang - 1998 - Journal of Symbolic Logic 63 (3):797 - 814.
    Related Works: Part II: C. T. Chong, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part II: Tame $\Sigma_2$ Coding and the Jump Operator. Ann. Pure Appl. Logic, vol. 87, no. 2, 103--116. Mathematical Reviews : MR1490049 Part III: C. T. Chong, Lei Qian, Theodore A. Slaman, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part III: Prompt Sets, Minimal Paries and Shoenfield's Conjecture. Mathematical Reviews : MR1818378.
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  9.  12
    The Degree of a Σn Cut.C. T. Chong & K. J. Mourad - 1990 - Annals of Pure and Applied Logic 48 (3):227-235.
  10.  35
    Minimal Upper Bounds for Ascending Sequences of Α-Recursively Enumerable Degrees.C. T. Chong - 1976 - Journal of Symbolic Logic 41 (1):250-260.
  11.  26
    The Minimal E-Degree Problem in Fragments of Peano Arithmetic.M. M. Arslanov, C. T. Chong, S. B. Cooper & Y. Yang - 2005 - Annals of Pure and Applied Logic 131 (1-3):159-175.
    We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () and prove the following results: in any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle.
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  12.  24
    1-Generic Degrees and Minimal Degrees in Higher Recursion Theory, II.C. T. Chong - 1986 - Annals of Pure and Applied Logic 31 (2):165-175.
  13.  11
    Degree Theory on ℵω.C. T. Chong & Sy D. Friedman - 1983 - Annals of Pure and Applied Logic 24 (1):87-97.
  14.  21
    Hyperhypersimple Supersets in Admissible Recursion Theory.C. T. Chong - 1983 - Journal of Symbolic Logic 48 (1):185-192.
  15.  34
    Meeting of the Association for Symbolic Logic: Singapore 1981.C. T. Chong - 1983 - Journal of Symbolic Logic 48 (3):893-897.
  16.  18
    An Α-Finite Injury Method of the Unbounded Type.C. T. Chong - 1976 - Journal of Symbolic Logic 41 (1):1-17.
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  17.  18
    Conference on Computability, Complexity and Randomness.Verónica Becher, C. T. Chong, Rod Downey, Noam Greenberg, Antonin Kucera, Bjørn Kjos-Hanssen, Steffen Lempp, Antonio Montalbán, Jan Reimann & Stephen Simpson - 2008 - Bulletin of Symbolic Logic 14 (4):548-549.
  18.  14
    Degree-Theoretic Bounds on the Morley Rank.C. T. Chong - 1987 - Archive for Mathematical Logic 26 (1):137-145.
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  19.  10
    Minimalα-hyperdegrees.C. T. Chong - 1984 - Archive for Mathematical Logic 24 (1):63-71.
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  20.  12
    Global and Local Admissibility: II. Major Subsets and Automorphisms.C. T. Chong - 1983 - Annals of Pure and Applied Logic 24 (2):99-111.
  21.  11
    Double Jumps of Minimal Degrees Over Cardinals.C. T. Chong - 1982 - Journal of Symbolic Logic 47 (2):329-334.
  22.  8
    Review: S. B. Cooper, T. A. Slaman, S. S. Wainer, Computability, Enumerability, Unsolvability, Directions in Recursion Theory. [REVIEW]C. T. Chong - 1999 - Journal of Symbolic Logic 64 (3):1362-1365.
  23.  7
    Nonstandard Models in Recursion Theory and Reverse Mathematics.C. T. Chong, Wei Li & Yue Yang - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models. and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey's Theorem for Pairs.
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  24.  7
    Preface.C. T. Chong & Y. C. Tay - 1997 - Annals of Pure and Applied Logic 84 (1):1.
  25.  8
    Maximal Chains in the Turing Degrees.C. T. Chong & Liang Yu - 2007 - Journal of Symbolic Logic 72 (4):1219 - 1227.
    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 (...)
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