31 found
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  1.  22
    Recursion-theoretic hierarchies.Peter G. Hinman - 1978 - New York: Springer Verlag.
  2.  19
    Density of the Medvedev lattice of Π0 1 classes.Douglas Cenzer & Peter G. Hinman - 2003 - Archive for Mathematical Logic 42 (6):583-600.
    The partial ordering of Medvedev reducibility restricted to the family of Π0 1 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π0 1 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.
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  3.  44
    A survey of Mučnik and Medvedev degrees.Peter G. Hinman - 2012 - Bulletin of Symbolic Logic 18 (2):161-229.
    We survey the theory of Mucnik and Medvedev degrees of subsets of $^{\omega}{\omega}$with particular attention to the degrees of $\Pi_{1}^{0}$ subsets of $^{\omega}2$. Sections 1-6 present the major definitions and results in a uniform notation. Sections 7-6 present proofs, some more complete than others, of the major results of the subject together with much of the required background material.
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  4.  45
    Some applications of forcing to hierarchy problems in arithmetic.Peter G. Hinman - 1969 - Mathematical Logic Quarterly 15 (20-22):341-352.
  5.  52
    Logical truth revisited.Peter G. Hinman, Jaegwon Kim & Stephen P. Stich - 1968 - Journal of Philosophy 65 (17):495-500.
    Thirty-two years ago W. V. Quine proposed a definition of 'logical truth' that has been widely repeated and reprinted. Quine himself seems to have recognized that this definition is wrong in detail; in section 1 we eliminate this fault. What has perhaps been less widely observed is that, in abandoning the model-theoretic account of logical truth in favor of a "substitutional" account, Quine's definition swells the ranks of the logical truths and makes the classification of a sentence as a logical (...)
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  6. (1 other version)Fundamentals of Mathematical Logic.Peter G. Hinman - 2007 - Bulletin of Symbolic Logic 13 (3):363-365.
  7.  6
    [Omnibus Review].Peter G. Hinman - 1972 - Journal of Symbolic Logic 37 (2):409-410.
  8.  45
    Degrees of difficulty of generalized r.e. separating classes.Douglas Cenzer & Peter G. Hinman - 2008 - Archive for Mathematical Logic 46 (7-8):629-647.
    Important examples of $\Pi^0_1$ classes of functions $f \in {}^\omega\omega$ are the classes of sets (elements of ω 2) which separate a given pair of disjoint r.e. sets: ${\mathsf S}_2(A_0, A_1) := \{f \in{}^\omega2 : (\forall i < 2)(\forall x \in A_i)f(x) \neq i\}$ . A wider class consists of the classes of functions f ∈ ω k which in a generalized sense separate a k-tuple of r.e. sets (not necessarily pairwise disjoint) for each k ∈ ω: ${\mathsf S}_k(A_0,\ldots,A_k-1) := (...)
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  9.  36
    Jump embeddings in the Turing degrees.Peter G. Hinman & Theodore A. Slaman - 1991 - Journal of Symbolic Logic 56 (2):563-591.
  10.  78
    Iterated relative recursive enumerability.Peter A. Cholak & Peter G. Hinman - 1994 - Archive for Mathematical Logic 33 (5):321-346.
    A result of Soare and Stob asserts that for any non-recursive r.e. setC, there exists a r.e.[C] setA such thatA⊕C is not of r.e. degree. A setY is called [of]m-REA (m-REA[C] [degree] iff it is [Turing equivalent to] the result of applyingm-many iterated ‘hops’ to the empty set (toC), where a hop is any function of the formX→X ⊕W e X . The cited result is the special casem=0,n=1 of our Theorem. Form=0,1, and any (m+1)-REA setC, ifC is not ofm-REA (...)
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  11.  19
    Meeting of the Association for Symbolic Logic, Chicago, 1985.Andreas Blass, Louise Hay & Peter G. Hinman - 1986 - Journal of Symbolic Logic 51 (2):507-510.
  12.  10
    (2 other versions)Hierarchies of Predicates of Finite Types.Peter G. Hinman - 1971 - Journal of Symbolic Logic 36 (1):146-147.
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  13.  22
    Generalized recursion theory.Jens Erik Fenstad & Peter G. Hinman (eds.) - 1974 - New York,: American Elsevier Pub. Co..
    Provability, Computability and Reflection.
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  14.  23
    Degrees of continuous functionals.Peter G. Hinman - 1973 - Journal of Symbolic Logic 38 (3):393-395.
    The partial order structure of degrees of unsolvability represented by continuous type-2 functionals is a proper extension of the partial order structure of type-1 degrees.
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  15.  7
    Hierarchies of Effective Descriptive Set Theory.Peter G. Hinman - 1972 - Journal of Symbolic Logic 37 (4):758-759.
  16.  6
    Omega Bibliography of Mathematical Logic: Volume 4, Recursion Theory.Peter G. Hinman (ed.) - 1987 - Berlin, Heidelberg, and New York: Springer.
    No categories
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  17.  13
    R. C. Lyndon. Existential Horn sentences. Proceedings of the American Mathematical Society, vol. 10 , pp. 994–998.Peter G. Hinman - 1965 - Journal of Symbolic Logic 30 (2):253.
  18.  8
    Ω-Bibliography of Mathematical Logic: Recursion Theory.Peter G. Hinman - 2013 - Springer.
    Gert H. Müller The growth of the number of publications in almost all scientific areas,· as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview ofthe existing literature, partic ularly if they do not have an extensive library available in their (...)
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  19.  8
    REVIEWS-Classical recursion theory, Volume II.P. Odifreddi & Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-72.
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  20.  15
    (1 other version)A. D. Tajmanov. O klassé modéléj, zamknutom otnositél'no prámogo proizvédéniá . Doklady Akadémii Nauk SSSR, vol. 127 , pp. 1173–1175. - A. D. Tajmanov. O klassé modéléj, zamknutyh otnositél'no prámogo proizvédéniá . Izvéstiá Akadémii Nauk SSSR, Sériá matématičéskaá, vol. 24 , pp. 493–510. [REVIEW]Peter G. Hinman - 1965 - Journal of Symbolic Logic 30 (2):253-254.
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  21.  33
    (1 other version)Bukowský L. and Příkry K.. Some matamathematical properties of measurable cardinals. Bulletin de l'Académie Polonaise des Sciences, Série des sciences mathématiques, astronomiques et physiques, vol. 14 , pp. 9–14. [REVIEW]Peter G. Hinman - 1968 - Journal of Symbolic Logic 33 (3):476-476.
  22.  15
    (1 other version)Fitting Melvin. Fundamentals of generalized recursion theory. Studies in logic and the foundations of mathematics, vol. 105. North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1981, xx + 307 pp. [REVIEW]Peter G. Hinman - 1986 - Journal of Symbolic Logic 51 (4):1078-1079.
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  23.  22
    Kozlova Z. I.. Aksioma konstruktivnosti i kratnaá otdélimost' i néotdélimost' v klassah analitičéskoj iérarhii . Sibirskij matématičéskij žurnal, vol. 5 , pp. 1239–1258. [REVIEW]Peter G. Hinman - 1973 - Journal of Symbolic Logic 38 (3):529-530.
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  24.  10
    (1 other version)Luis E. Sanchis. Recursive functional. Studies in logic and the foundations of mathematics, vol. 131. North-Holland, Amsterdam etc. 1992, xii + 277 pp. [REVIEW]Peter G. Hinman - 1993 - Journal of Symbolic Logic 58 (4):1468-1469.
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  25.  30
    (2 other versions)Normann Dag. Recursion on the countable functionals. Lecture notes in mathematics, vol. 811. Springer-Verlag, Berlin, Heidelberg, and New York, 1980, VIII + 191 pp.Normann Dag. The continuous functionals; computations, recursions and degrees. Annals of mathematical logic, vol. 21 , pp. 1–26. [REVIEW]Peter G. Hinman - 1984 - Journal of Symbolic Logic 49 (2):668-670.
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  26.  17
    (1 other version)P. G. Odifreddi. Classical recursion theory. Volume II. Studies in logic and the foundations of mathematics, vol. 143. Elsevier, Amsterdam etc. 1999, xvi + 949 pp. [REVIEW]Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
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  27.  18
    (2 other versions)Piergiorgio Odifreddi. Classical recursion theory. The theory of functions and sets of natural numbers. Studies in logic and the foundations of mathematics, vol. 125. North-Holland, Amsterdam etc. 1989, xvii + 668 pp. [REVIEW]Peter G. Hinman - 1990 - Journal of Symbolic Logic 55 (3):1307-1308.
  28.  8
    (1 other version)Review: Petr Vopenka, Die Konstruktion von Modellen der Mengenlehre Nach der Methode der Ultraprodukte. [REVIEW]Peter G. Hinman - 1968 - Journal of Symbolic Logic 33 (3):475-476.
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  29. Review: R. C. Lyndon, Existential Horn Sentences. [REVIEW]Peter G. Hinman - 1965 - Journal of Symbolic Logic 30 (2):253-253.
  30.  8
    (1 other version)Review: Yiannis N. Moschovakis, Hyperanalytic Predicates; Thomas J. Grilliot, Hierarchies Based on Objects of Finite Type. [REVIEW]Peter G. Hinman - 1971 - Journal of Symbolic Logic 36 (1):147-148.
  31.  22
    V. I. Amstislavskij. Téorétiko-množéstvénnyé operacii i rékursivnyé iérarhii. Doklady Akadémii Nauk SSSR, vol. 169 , pp. 995–998. - V. I. Amstislavskij. Set-theoretical operations and recursive hierarchies. English translation of the preceding by E. Wesley. Soviet mathematics, vol. 7 no. 4 , pp. 1029–1032. - V. I. Amstislavskij. Rasširénié rékursivnyh iérarhij i R-opéracii. Doklady Akadémii Nauk SSSR, vol. 180 , pp. 1023–1026. - V. I. Amstislavskij. Expansion of recursive hierarchies and R-operations. English translation of the preceding by A. Yablonsky. Soviet mathematics, vol. 9 no. 3 , pp. 703–706. - V. I. Amstislavskij. O razložénii téla množéstv, polučaémyh R-opéraciéj nad rékursivnymi množéstvami. Doklady Akadémii Nauk SSSR, vol. 191 , pp. 743–746. - V. I. Amstislavskij. On the decomposition of a field of sets obtained by an R-operation over recursive sets. English translation of the preceding by S. Shepherd. Soviet mathematics, vol. 11 no. 2 , pp. 419–422. - V. I. Amstislavskij. [REVIEW]Peter G. Hinman - 1972 - Journal of Symbolic Logic 37 (2):409-410.
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