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  1.  3
    Peter G. Hinman (1978). Recursion-Theoretic Hierarchies. Springer-Verlag.
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  2.  14
    Peter G. Hinman (2012). A Survey of Mučnik and Medvedev Degrees. 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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  3.  14
    Peter G. Hinman (1969). Some Applications of Forcing to Hierarchy Problems in Arithmetic. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (20-22):341-352.
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  4.  4
    Douglas Cenzer & Peter G. Hinman (2003). Density of the Medvedev Lattice of Π0 1 Classes. 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.  6
    Douglas Cenzer & Peter G. Hinman (2008). Degrees of Difficulty of Generalized R.E. Separating Classes. 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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  6.  4
    Peter G. Hinman (1969). Some Applications of Forcing to Hierarchy Problems in Arithmetic. Mathematical Logic Quarterly 15 (20‐22):341-352.
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  7.  14
    Peter A. Cholak & Peter G. Hinman (1994). Iterated Relative Recursive Enumerability. 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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  8.  3
    Douglas Cenzer & Peter G. Hinman (2003). Density of the Medvedev Lattice of Π [Sup0][Sub1]. Archive for Mathematical Logic 42 (6):583-600.
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  9. Peter G. Hinman (2007). Fundamentals of Mathematical Logic. Bulletin of Symbolic Logic 13 (3):363-365.
     
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  10.  11
    Peter G. Hinman, Jaegwon Kim & Stephen P. Stich (1968). Logical Truth Revisited. Journal of Philosophy 65 (17):495-500.
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  11.  2
    Peter G. Hinman & Theodore A. Slaman (1991). Jump Embeddings in the Turing Degrees. Journal of Symbolic Logic 56 (2):563-591.
  12.  1
    Peter G. Hinman (1965). Lyndon R. C.. Existential Horn Sentences. Proceedings of the American Mathematical Society, Vol. 10 , Pp. 994–998. Journal of Symbolic Logic 30 (2):253.
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  13.  10
    Andreas Blass, Louise Hay & Peter G. Hinman (1986). Meeting of the Association for Symbolic Logic: Chicago, 1985. Journal of Symbolic Logic 51 (2):507-510.
  14.  6
    Peter G. Hinman (1973). Degrees of Continuous Functionals. 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.  2
    Peter G. Hinman (1968). Review: L. Bukowsky, K. Prikry, Some Metamathematical Properties of Measurable Cardinals. [REVIEW] Journal of Symbolic Logic 33 (3):476-476.
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  16.  2
    Peter G. Hinman (1971). Review: D. A. Clarke, Hierarchies of Predicates of Finite Types. [REVIEW] Journal of Symbolic Logic 36 (1):146-147.
  17.  1
    Peter G. Hinman (1972). Hierarchies of Effective Descriptive Set Theory. Journal of Symbolic Logic 37 (4):758-759.
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  18.  2
    Peter G. Hinman (1990). Review: Piergiorgio Odifreddi, Classical Recursion Theory. The Theory of Functions and Sets of Natural Numbers. [REVIEW] Journal of Symbolic Logic 55 (3):1307-1308.
  19.  1
    Peter G. Hinman (1993). Review: Luis E. Sanchis, Recursive Functionals. [REVIEW] Journal of Symbolic Logic 58 (4):1468-1469.
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  20.  1
    Peter G. Hinman (2001). Review: P. G. Odifreddi, Classical Recursion Theory. [REVIEW] Bulletin of Symbolic Logic 7 (1):71-73.
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  21.  1
    Peter G. Hinman (1968). Review: Petr Vopenka, Die Konstruktion von Modellen der Mengenlehre Nach der Methode der Ultraprodukte. [REVIEW] Journal of Symbolic Logic 33 (3):475-476.
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  22.  1
    Peter G. Hinman (1986). Review: Melvin Fitting, Fundamentals of Generalized Recursion Theory. [REVIEW] Journal of Symbolic Logic 51 (4):1078-1079.
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  23. Andreas Blass, Louise Hay & Peter G. Hinman (1986). Meeting of the Association for Symbolic Logic, Chicago, 1985. Journal of Symbolic Logic 51 (2):507-510.
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  24.  3
    Jens Erik Fenstad & Peter G. Hinman (eds.) (1974). Generalized Recursion Theory. New York,American Elsevier Pub. Co..
    Provability, Computability and Reflection.
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  25. Peter G. Hinman (1965). 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] Journal of Symbolic Logic 30 (2):253-254.
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  26. Peter G. Hinman (1972). Amstislavskij V. I.. Téorétiko-Množéstvénnyé Operacii I Rékursivnyé Iérarhii. Doklady Akadémii Nauk SSSR, Vol. 169 , Pp. 995–998.Amstislavskij V. I.. Set-Theoretical Operations and Recursive Hierarchies. English Translation of the Preceding by E. Wesley. Soviet Mathematics, Vol. 7 No. 4 , Pp. 1029–1032.Amstislavskij V. I.. Rasširénié Rékursivnyh Iérarhij I R-Opéracii. Doklady Akadémii Nauk SSSR, Vol. 180 , Pp. 1023–1026.Amstislavskij V. I.. Expansion of Recursive Hierarchies and R-Operations. English Translation of the Preceding by A. Yablonsky. Soviet Mathematics, Vol. 9 No. 3 , Pp. 703–706.Amstislavskij V. I.. O Razložénii Téla Množéstv, Polučaémyh R-Opéraciéj Nad Rékursivnymi Množéstvami. Doklady Akadémii Nauk SSSR, Vol. 191 , Pp. 743–746.Amstislavskij V. I.. 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.Amstislavskij V. I.. Efféktivnyé R-Mno. [REVIEW] Journal of Symbolic Logic 37 (2):409-410.
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  27. Peter G. Hinman (1968). 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] Journal of Symbolic Logic 33 (3):476.
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  28. Peter G. Hinman (1971). 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] Journal of Symbolic Logic 36 (1):146-147.
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  29. Peter G. Hinman (2001). Classical Recursion Theory. Bulletin of Symbolic Logic 7 (1):71-73.
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  30. Peter G. Hinman (1986). 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] Journal of Symbolic Logic 51 (4):1078-1079.
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  31. Peter G. Hinman (1973). Kozlova Z. I.. Aksioma konstruktivnosti i kratnaá otdélimost' i néotdélimost' v klassah analitičéskoj iérarhii . Sibirskij matématičéskij žurnal, vol. 5 , pp. 1239–1258. [REVIEW] Journal of Symbolic Logic 38 (3):529-530.
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  32. Peter G. Hinman (1971). Moschovakis Yiannis N.. Hyperanalytic Predicates. Transactions of the American Mathematical Society, Vol. 129 , Pp. 249–282.Grilliot Thomas J.. Hierarchies Based on Objects of Finite Type. [REVIEW] Journal of Symbolic Logic 36 (1):147-148.
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  33. Peter G. Hinman (1984). 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] Journal of Symbolic Logic 49 (2):668-670.
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  34. Peter G. Hinman (1990). Odifreddi Piergiorgio. 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] Journal of Symbolic Logic 55 (3):1307-1308.
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  35. Peter G. Hinman (1972). [Omnibus Review]. Journal of Symbolic Logic 37 (2):409-410.
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  36. Peter G. Hinman (1965). Review: A. D. Tajmanov, On a Class of Models, Closed with Respect to Direct Product. [REVIEW] Journal of Symbolic Logic 30 (2):253-254.
     
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  37. Peter G. Hinman (1984). Review: Dag Normann, Recursion on the Countable Functionals; Dag Normann, The Continuous Functionals; Computations, Recursions and Degrees. [REVIEW] Journal of Symbolic Logic 49 (2):668-670.
     
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  38. Peter G. Hinman (1965). Review: R. C. Lyndon, Existential Horn Sentences. [REVIEW] Journal of Symbolic Logic 30 (2):253-253.
     
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  39. Peter G. Hinman (1971). Review: Yiannis N. Moschovakis, Hyperanalytic Predicates; Thomas J. Grilliot, Hierarchies Based on Objects of Finite Type. [REVIEW] Journal of Symbolic Logic 36 (1):147-148.
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  40. Peter G. Hinman (1973). Review: Z. I. Kozlova, The Axiom of Constructibility and Multiple Separability and Inseparability in the Classes of the Analytical Hierarchy. [REVIEW] Journal of Symbolic Logic 38 (3):529-530.
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  41. Peter G. Hinman (1993). Sanchis Luis E.. Recursive Functional. Studies in Logic and the Foundations of Mathematics, Vol. 131. North-Holland, Amsterdam Etc. 1992, Xii + 277 Pp. [REVIEW] Journal of Symbolic Logic 58 (4):1468-1469.
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  42. Peter G. Hinman (1968). Vopěnka Petr. Postroénié modeléj téorii mnozéstv métodom ul'traproizvédéniá . Zeitschrift für mathematische Logik und Grundtagen der Mathematik, vol. 8 , pp. 293–304. [REVIEW] Journal of Symbolic Logic 33 (3):475-476.
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  43. G. H. Müller, Wolfgang Lenski & Peter G. Hinman (1987). [Omega]-Bibliography of Mathematical Logic.
     
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  44. P. Odifreddi & Peter G. Hinman (2001). REVIEWS-Classical Recursion Theory, Volume II. Bulletin of Symbolic Logic 7 (1):71-72.
     
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