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Peter Clote [10]Peter G. Clote [2]
  1. Samuel R. Buss & Peter Clote (1996). Cutting Planes, Connectivity, and Threshold Logic. Archive for Mathematical Logic 35 (1):33-62.
    Originating from work in operations research the cutting plane refutation systemCP is an extension of resolution, where unsatisfiable propositional logic formulas in conjunctive normal form are recognized by showing the non-existence of boolean solutions to associated families of linear inequalities. Polynomial sizeCP proofs are given for the undirecteds-t connectivity principle. The subsystemsCP q ofCP, forq≥2, are shown to be polynomially equivalent toCP, thus answering problem 19 from the list of open problems of [8]. We present a normal form theorem forCP (...)
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  2. Peter Clote (1995). Editor's Introduction. Notre Dame Journal of Formal Logic 36 (4):499-501.
    This collection of articles on Models of Arithmetic is dedicated to the memory of Zygmunt Ratajczyk, who contributed a number of important results to the field, and who unexpectedly died in February 1994.
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  3. Peter Clote (1990). Review: Wilfried Sieg, Georg Dorn, P. Weingartner, Reductions of Theories for Analysis. [REVIEW] Journal of Symbolic Logic 55 (1):354-354.
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  4. Peter Clote (1990). Sieg Wilfried. Reductions of Theories for Analysis. Foundations of Logic and Linguistics, Problems and Their Solutions, Edited by Dorn Georg and Weingartner P., Plenum Press, New York and London 1985, Pp. 199–231. [REVIEW] Journal of Symbolic Logic 55 (1):354-354.
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  5. Peter Clote (1989). Modèles Non Standard En Arithmétique Et Théorie des Ensembles, Publications Mathématiques de l'Université Paris VII, No. 22, UER de Mathématiques, Paris 1987, 147 Pp. [REVIEW] Journal of Symbolic Logic 54 (1):284-287.
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  6. Peter Clote (1989). Review: , Modeles non Standard en Arithmetique et theorie des Ensembles; A. J. Wilkie, Modeles non Standard de L'Arithmetique, et Complexite Algorithmique; J.-P. Ressayre, Modeles non Standard et Sous-Systemes Remarquables de ZF. [REVIEW] Journal of Symbolic Logic 54 (1):284-287.
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  7. Peter G. Clote (1987). Review: Harvey M. Friedman, Stephen G. Simpson, Rick L. Smith, Countable Algebra and Set Existence Axioms; Harvey M. Friedman, Stephen G. Simpson, Rick L. Smith, Addendum to "Countable Algebra and Set Existence Axioms.". [REVIEW] Journal of Symbolic Logic 52 (1):276-278.
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  8. Peter G. Clote (1987). Review: Wilfried Sieg, Fragments of Arithmetic. [REVIEW] Journal of Symbolic Logic 52 (4):1054-1055.
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  9. Douglas Cenzer, Peter Clote, Rick L. Smith, Robert I. Soare & Stanley S. Wainer (1986). Members of Countable Π10 Classes. Annals of Pure and Applied Logic 31:145-163.
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  10. Peter Clote (1986). A Generalization of the Limit Lemma and Clopen Games. Journal of Symbolic Logic 51 (2):273-291.
    We give a new characterization of the hyperarithmetic sets: a set X of integers is recursive in e α if and only if there is a Turing machine which computes X and "halts" in less than or equal to the ordinal number ω α of steps. This result represents a generalization of the well-known "limit lemma" due to J. R. Shoenfield [Sho-1] and later independently by H. Putnam [Pu] and independently by E. M. Gold [Go]. As an application of this (...)
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  11. Peter Clote (1984). A Recursion Theoretic Analysis of the Clopen Ramsey Theorem. Journal of Symbolic Logic 49 (2):376-400.
    Solovay has shown that if F: [ω] ω → 2 is a clopen partition with recursive code, then there is an infinite homogeneous hyperarithmetic set for the partition (a basis result). Simpson has shown that for every 0 α , where α is a recursive ordinal, there is a clopen partition F: [ω] ω → 2 such that every infinite homogeneous set is Turing above 0 α (an anti-basis result). Here we refine these results, by associating the "order type" of (...)
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  12. Peter Clote & Kenneth Mcaloon (1983). Two Further Combinatorial Theorems Equivalent to the 1-Consistency of Peano Arithmetic. Journal of Symbolic Logic 48 (4):1090-1104.
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