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  1. 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 (weak) and Medvedev (strong) 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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  2. 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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  3. 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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  4. Douglas Cenzer & Peter G. Hinman (2003). Density of the Medvedev Lattice of Π [Sup0][Sub1]. Archive for Mathematical Logic 42 (6).
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  5. Peter G. Hinman (2001). Review: P. G. Odifreddi, Classical Recursion Theory. [REVIEW] Bulletin of Symbolic Logic 7 (1):71-73.
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  6. P. Odifreddi & Peter G. Hinman (2001). REVIEWS-Classical Recursion Theory, Volume II. Bulletin of Symbolic Logic 7 (1):71-72.
     
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  7. 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. Peter G. Hinman (1993). Review: Luis E. Sanchis, Recursive Functionals. [REVIEW] Journal of Symbolic Logic 58 (4):1468-1469.
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  9. Peter G. Hinman & Theodore A. Slaman (1991). Jump Embeddings in the Turing Degrees. Journal of Symbolic Logic 56 (2):563-591.
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  10. 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.
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  11. 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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  12. 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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  13. 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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  14. Peter G. Hinman (1978). Recursion-Theoretic Hierarchies. Springer-Verlag.
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  15. 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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  16. 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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  17. 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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  18. Peter G. Hinman (1972). [Omnibus Review]. Journal of Symbolic Logic 37 (2):409-410.
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  19. Peter G. Hinman (1971). Review: D. A. Clarke, Hierarchies of Predicates of Finite Types. [REVIEW] Journal of Symbolic Logic 36 (1):146-147.
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  20. 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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  21. 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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  22. 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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  23. 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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  24. Peter G. Hinman, Jaegwon Kim & Stephen P. Stich (1968). Logical Truth Revisited. Journal of Philosophy 65 (17):495-500.
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  25. 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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  26. Peter G. Hinman (1965). Review: R. C. Lyndon, Existential Horn Sentences. [REVIEW] Journal of Symbolic Logic 30 (2):253-253.
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