47 found
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  1.  17
    Recursion-theoretic hierarchies.Peter G. Hinman - 1978 - New York: Springer Verlag.
  2.  36
    Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
  3.  14
    Classical Recursion Theory. The Theory of Functions and Sets of Natural Numbers.Peter G. Hinman - 1990 - Journal of Symbolic Logic 55 (3):1307-1308.
  4.  12
    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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  5.  33
    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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  6.  17
    Density of the Medvedev lattice of Π01 classes.Douglas Cenzer & Peter G. Hinman - 2003 - Archive for Mathematical Logic 42 (6):583-600.
    Abstract.The partial ordering of Medvedev reducibility restricted to the family of Π01 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π01 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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  7.  13
    Some applications of forcing to hierarchy problems in arithmetic.Peter G. Hinman - 1969 - Mathematical Logic Quarterly 15 (20‐22):341-352.
  8.  36
    Some applications of forcing to hierarchy problems in arithmetic.Peter G. Hinman - 1969 - Mathematical Logic Quarterly 15 (20-22):341-352.
  9.  47
    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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  10. Fundamentals of Mathematical Logic.Peter G. Hinman - 2007 - Bulletin of Symbolic Logic 13 (3):363-365.
  11.  5
    [Omnibus Review].Peter G. Hinman - 1972 - Journal of Symbolic Logic 37 (2):409-410.
  12.  39
    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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  13.  19
    Jump embeddings in the Turing degrees.Peter G. Hinman & Theodore A. Slaman - 1991 - Journal of Symbolic Logic 56 (2):563-591.
  14.  68
    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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  15.  11
    Recursion on the Countable Functionals.Peter G. Hinman - 1984 - Journal of Symbolic Logic 49 (2):668-670.
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  16.  34
    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.
  17.  16
    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.
  18.  4
    Hierarchies of Predicates of Finite Types.Peter G. Hinman - 1971 - Journal of Symbolic Logic 36 (1):146-147.
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  19.  19
    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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  20.  21
    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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  21.  4
    Hierarchies of Effective Descriptive Set Theory.Peter G. Hinman - 1972 - Journal of Symbolic Logic 37 (4):758-759.
  22.  5
    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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  23.  16
    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.
  24.  5
    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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  25.  4
    REVIEWS-Classical recursion theory, Volume II.P. Odifreddi & Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-72.
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  26.  10
    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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  27.  26
    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.
  28.  11
    Clarke D. A.. Hierarchies of predicates of finite types. Memoirs of the American Mathematical Society, no. 51. American Mathematical Society, Providence 1964, 95 pp. [REVIEW]Peter G. Hinman - 1971 - Journal of Symbolic Logic 36 (1):146-147.
  29.  10
    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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  30.  14
    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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  31.  10
    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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  32.  26
    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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  33.  13
    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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  34.  14
    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.
  35. Review: A. D. Tajmanov, On a Class of Models, Closed with Respect to Direct Product. [REVIEW]Peter G. Hinman - 1965 - Journal of Symbolic Logic 30 (2):253-254.
  36.  6
    Review: D. A. Clarke, Hierarchies of Predicates of Finite Types. [REVIEW]Peter G. Hinman - 1971 - Journal of Symbolic Logic 36 (1):146-147.
  37. Review: Dag Normann, Recursion on the Countable Functionals; Dag Normann, The Continuous Functionals; Computations, Recursions and Degrees. [REVIEW]Peter G. Hinman - 1984 - Journal of Symbolic Logic 49 (2):668-670.
     
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  38.  5
    Review: L. Bukowsky, K. Prikry, Some Metamathematical Properties of Measurable Cardinals. [REVIEW]Peter G. Hinman - 1968 - Journal of Symbolic Logic 33 (3):476-476.
  39.  4
    Review: Luis E. Sanchis, Recursive Functionals. [REVIEW]Peter G. Hinman - 1993 - Journal of Symbolic Logic 58 (4):1468-1469.
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  40.  8
    Review: Melvin Fitting, Fundamentals of Generalized Recursion Theory. [REVIEW]Peter G. Hinman - 1986 - Journal of Symbolic Logic 51 (4):1078-1079.
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  41.  10
    Review: Piergiorgio Odifreddi, Classical Recursion Theory. The Theory of Functions and Sets of Natural Numbers. [REVIEW]Peter G. Hinman - 1990 - Journal of Symbolic Logic 55 (3):1307-1308.
  42.  5
    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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  43. Review: R. C. Lyndon, Existential Horn Sentences. [REVIEW]Peter G. Hinman - 1965 - Journal of Symbolic Logic 30 (2):253-253.
  44.  4
    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.
  45.  20
    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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  46.  6
    Vopěnka Petr. Postroénié modeléj téorii mnozéstv métodom ul'traproizvédéniá . Zeitschrift für mathematische Logik und Grundtagen der Mathematik, vol. 8 , pp. 293–304. [REVIEW]Peter G. Hinman - 1968 - Journal of Symbolic Logic 33 (3):475-476.
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  47.  12
    Yiannis N. Moschovakis. Hyperanalytic predicates. Transactions of the American Mathematical Society, vol. 129 , pp. 249–282. - Thomas J. Grilliot. Hierarchies based on objects of finite type. The journal of symbolic logic, vol. 34 , pp. 177–182. [REVIEW]Peter G. Hinman - 1971 - Journal of Symbolic Logic 36 (1):147-148.
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