Search results for 'Reducibility' (try it on Scholar)

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  1.  43
    John Bacon (1986). Supervenience, Necessary Coextensions, and Reducibility. Philosophical Studies 49 (March):163-76.
    Supervenience in most of its guises entails necessary coextension. Thus theoretical supervenience entails nomically necessary coextension. Kim's result, thus strengthened, has yet to hit home. I suspect that many supervenience enthusiasts would cool at necessary coextension: they didn't mean to be saying anything quite so strong. Furthermore, nomically necessary coextension can be a good reason for property identification, leading to reducibility in principle. This again is more than many supervenience theorists bargained for. They wanted supervenience without reducibility. It (...)
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  2.  4
    Daniele Marsibilio & Andrea Sorbi (2012). Bounded Enumeration Reducibility and its Degree Structure. Archive for Mathematical Logic 51 (1-2):163-186.
    We study a strong enumeration reducibility, called bounded enumeration reducibility and denoted by ≤be, which is a natural extension of s-reducibility ≤s. We show that ≤s, ≤be, and enumeration reducibility do not coincide on the ${\Pi^0_1}$ –sets, and the structure ${\boldsymbol{\mathcal{D}_{\rm be}}}$ of the be-degrees is not elementarily equivalent to the structure of the s-degrees. We show also that the first order theory of ${\boldsymbol{\mathcal{D}_{\rm be}}}$ is computably isomorphic to true second order arithmetic: this answers an (...)
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  3.  12
    Dieter Spreen (2005). Strong Reducibility of Partial Numberings. Archive for Mathematical Logic 44 (2):209-217.
    A strong reducibility relation between partial numberings is introduced which is such that the reduction function transfers exactly the numbers which are indices under the numbering to be reduced into corresponding indices of the other numbering. The degrees of partial numberings of a given set with respect to this relation form an upper semilattice.In addition, Ershov’s completion construction for total numberings is extended to the partial case: every partially numbered set can be embedded in a set which results from (...)
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  4.  2
    David Duarte (2015). Analogy and Balancing: The Partial Reducibility Thesis and Its Problems. Revus 25:141-154.
    With an analysis of the structure and the sequence of analogy, the paper is mainly a critique to the partial reducibility thesis: a thesis sustaining that analogy, besides a strictly analogical step, is in the remaining part reducible to balancing. Thus, the paper points out some problems raised by the partial reducibility thesis, such as the contingency of reducibility or the fact that a proper analogy is done under the cover of a balancing. The main point is, (...)
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  5.  1
    Karol Habart & K. Habart (1992). Bounds in the Turing Reducibility of Functions. Mathematical Logic Quarterly 38 (1):423-430.
    A hierarchy of functions with respect to their role as bounds in the Turing reducibility of functions is introduced and studied. This hierarchy leads to a certain notion of incompressibility of sets which is also investigated.
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  6.  2
    Martin Koerwien (2009). Comparing Borel Reducibility and Depth of an Ω-Stable Theory. Notre Dame Journal of Formal Logic 50 (4):365-380.
    In "A proof of Vaught's conjecture for ω-stable theories," the notions of ENI-NDOP and eni-depth have been introduced, which are variants of the notions of NDOP and depth known from Shelah's classification theory. First, we show that for an ω-stable first-order complete theory, ENI-NDOP allows tree decompositions of countable models. Then we discuss the relationship between eni-depth and the complexity of the isomorphism relation for countable models of such a theory in terms of Borel reducibility as introduced by Friedman (...)
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  7.  26
    B. R. George (2013). Knowing‐'Wh', Mention‐Some Readings, and Non‐Reducibility. Thought: A Journal of Philosophy 2 (2):166-177.
    This article presents a new criticisms of reductive approaches to knowledge-‘wh’ (i.e., those approaches on which whether one stands in the knowledge-‘wh’ relation to a question is determined by whether one stands in the knowledge-‘that’ relation to some answer(s) to the question). It argues in particular that the truth of a knowledge-‘wh’ attribution like ‘Janna knows where she can buy an Italian newspaper’ depends not only on what Janna knows about the availability of Italian newspapers, but on what she believes (...)
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  8.  6
    Fuad Aleskerov & Yetkin Çinar (2008). 'Q-Pareto-Scalar' Two-Stage Extremization Model and its Reducibility to One-Stage Model. Theory and Decision 65 (4):325-338.
    A two-stage sequential choice model is studied, the first stage being defined by q-Pareto multicriterial choice rule, and the second stage being defined by scalar extremization model. In this model, at the first stage the q-Pareto rule choses alternatives which are not only undominated in terms of Pareto comparison, but also includes into choice the alternatives which are dominated by no more than q alternatives. Since the choice set of the first-stage usually contains too many elements, obtained set is used (...)
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  9.  6
    Kate Copestake (1997). On Nondeterminism, Enumeration Reducibility and Polynomial Bounds. Mathematical Logic Quarterly 43 (3):287-310.
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  10.  5
    Quinn Culver (2014). Polynomial Clone Reducibility. Archive for Mathematical Logic 53 (1-2):1-10.
    Polynomial clone reducibilities are generalizations of the truth-table reducibilities. A polynomial clone is a set of functions over a finite set X that is closed under composition and contains all the constant and projection functions. For a fixed polynomial clone ${\fancyscript{C}}$ , a sequence ${B\in X^{\omega}}$ is ${\fancyscript{C}}$ -reducible to ${A \in {X}^{\omega}}$ if there is an algorithm that computes B from A using only effectively selected functions from ${\fancyscript{C}}$ . We show that if A is Kurtz random and ${\fancyscript{C}_{1} (...)
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  11.  4
    Sui Yuefei (1994). A New Reducibility Between Turing‐ and Wtt‐Reducibility. Mathematical Logic Quarterly 40 (1):106-110.
    The project was partially supported by a NSF grant of China. The author was grateful to Professor S. Lempp for his encouragement and suggestion while the author was visiting the Department of Mathematics at the University of Wisconsin.
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  12. Harvey Friedman, Borel and Baire Reducibility.
    The Borel reducibility theory of Polish equivalence relations, at least in its present form, was initiated independently in [FS89] and [HKL90]. There is now an extensive literature on this topic, including fundamental work on the Glimm-Effros dichotomy in [HKL90], on countable Borel equivalence relations in [DJK94], and on Polish group actions in [BK96].
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  13.  10
    Vasco Brattka (2005). Effective Borel Measurability and Reducibility of Functions. Mathematical Logic Quarterly 51 (1):19-44.
    The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for single-valued as well as for multi-valued functions by a direct effectivization of the classical definition. On Baire space the finite levels of the resulting hierarchy of functions can be characterized using a notion of reducibility for functions and corresponding complete (...)
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  14.  17
    Rodolfo Gambini, Lucía Lewowicz & Jorge Pullin (2015). Quantum Mechanics, Strong Emergence and Ontological Non-Reducibility. Foundations of Chemistry 17 (2):117-127.
    We show that a new interpretation of quantum mechanics, in which the notion of event is defined without reference to measurement or observers, allows to construct a quantum general ontology based on systems, states and events. Unlike the Copenhagen interpretation, it does not resort to elements of a classical ontology. The quantum ontology in turn allows us to recognize that a typical behavior of quantum systems exhibits strong emergence and ontological non-reducibility. Such phenomena are not exceptional but natural, and (...)
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  15.  15
    Harvey Friedman & Lee Stanley (1989). A Borel Reducibility Theory for Classes of Countable Structures. Journal of Symbolic Logic 54 (3):894-914.
    We introduce a reducibility preordering between classes of countable structures, each class containing only structures of a given similarity type (which is allowed to vary from class to class). Though we sometimes work in a slightly larger context, we are principally concerned with the case where each class is an invariant Borel class (i.e. the class of all models, with underlying set $= \omega$, of an $L_{\omega_1\omega}$ sentence; from this point of view, the reducibility can be thought of (...)
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  16.  5
    Longyun Ding (2011). Borel Reducibility and Finitely Hölder (Α) Embeddability. Annals of Pure and Applied Logic 162 (12):970-980.
    Let , be a sequence of pseudo-metric spaces, and let p≥1. For , let . For Borel reducibility between equivalence relations , we show it is closely related to finitely Hölder embeddability between pseudo-metric spaces.
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  17.  13
    Johanna N. Y. Franklin & Frank Stephan (2010). Schnorr Trivial Sets and Truth-Table Reducibility. Journal of Symbolic Logic 75 (2):501-521.
    We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak truth-table degrees. This answers a question of Downey, Griffiths and LaForte.
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  18.  5
    R. Downey, G. LaForte & A. Nies (1998). Computably Enumerable Sets and Quasi-Reducibility. Annals of Pure and Applied Logic 95 (1-3):1-35.
    We consider the computably enumerable sets under the relation of Q-reducibility. We first give several results comparing the upper semilattice of c.e. Q-degrees, RQ, Q, under this reducibility with the more familiar structure of the c.e. Turing degrees. In our final section, we use coding methods to show that the elementary theory of RQ, Q is undecidable.
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  19.  57
    Karl-Georg Niebergall (2000). On the Logic of Reducibility: Axioms and Examples. [REVIEW] Erkenntnis 53 (1-2):27-61.
    This paper is an investigation into what could be a goodexplication of ``theory S is reducible to theory T''''. Ipresent an axiomatic approach to reducibility, which is developedmetamathematically and used to evaluate most of the definitionsof ``reducible'''' found in the relevant literature. Among these,relative interpretability turns out to be most convincing as ageneral reducibility concept, proof-theoreticalreducibility being its only serious competitor left. Thisrelation is analyzed in some detail, both from the point of viewof the reducibility axioms and (...)
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  20.  5
    René David (2001). Normalization Without Reducibility. Annals of Pure and Applied Logic 107 (1-3):121-130.
    In [gallier], general results (due to Coppo, Dezani and Veneri) relating properties of pure lambda terms and their typability in some systems with conjunctive types are proved in a uniform way by using the reducibility method.This paper gives a very short proof of the same results (actually, one of them is a bit stronger) using purely arithmetical methods.
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  21.  3
    Longyun Ding (2012). Borel Reducibility and Hölder(Α) Embeddability Between Banach Spaces. Journal of Symbolic Logic 77 (1):224-244.
    We investigate Borel reducibility between equivalence relations $E(X;p)=X^{\mathbb{N}}/\ell_{p}(X)'s$ where X is a separable Banach space. We show that this reducibility is related to the so called Hölder(α) embeddability between Banach spaces. By using the notions of type and cotype of Banach spaces, we present many results on reducibility and unreducibility between E(L r ; p)'s and E(c 0 ; p)'s for r, p ∈ [1, +∞). We also answer a problem presented by Kanovei in the affirmative by (...)
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  22.  13
    Steffen Lempp & Manuel Lerman (1992). The Existential Theory of the Poset of R.E. Degrees with a Predicate for Single Jump Reducibility. Journal of Symbolic Logic 57 (3):1120-1130.
    We show the decidability of the existential theory of the recursively enumerable degrees in the language of Turing reducibility, Turing reducibility of the Turing jumps, and least and greatest element.
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  23.  12
    E. Hermann (1992). 1-Reducibility Inside an M-Degree with Maximal Set. Journal of Symbolic Logic 57 (3):1046-1056.
    The structure of the l-degrees included in an m-degree with a maximal set together with the l-reducibility relation is characterized. For this a special sublattice of the lattice of recursively enumerable sets under the set-inclusion is used.
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  24.  3
    C. J. Ash (1992). Generalizations of Enumeration Reducibility Using Recursive Infinitary Propositional Sentences. Annals of Pure and Applied Logic 58 (3):173-184.
    Ash, C.J., Generalizations of enumeration reducibility using recursive infinitary propositional sentences, Annals of Pure and Applied Logic 58 173–184. We consider the relation between sets A and B that for every set S if A is Σ0α in S then B is Σ0β in S. We show that this is equivalent to the condition that B is definable from A in a particular way involving recursive infinitary propositional sentences. When α = β = 1, this condition is that B (...)
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  25.  10
    Douglas Cenzer (1984). Monotone Reducibility and the Family of Infinite Sets. Journal of Symbolic Logic 49 (3):774-782.
    Let A and B be subsets of the space 2 N of sets of natural numbers. A is said to be Wadge reducible to B if there is a continuous map Φ from 2 N into 2 N such that A = Φ -1 (B); A is said to be monotone reducible to B if in addition the map Φ is monotone, that is, $a \subset b$ implies $\Phi (a) \subset \Phi(b)$ . The set A is said to be monotone (...)
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  26.  3
    A. N. Degtev (1993). On P-Reducibility of Numerations. Annals of Pure and Applied Logic 63 (1):57-60.
    Degtev, A.N., On p-reducibility of numerations, Annals of Pure and Applied Logic 63 57–60. If α and β are two numerations of a set S, then αpβ if there exists a total recursive function f such that [s ε S][α-1=[x:[y ε Df][Dyβ-1]]], where Dn is a finite set with canonical number n. It is proved that if α and β are two computable numerations of some family of recursively enumerable sets A and αpβ, then there is a computable numeration, (...))
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  27.  3
    Juichi Shinoda (1997). Strong Polynomial-Time Reducibility. Annals of Pure and Applied Logic 84 (1):97-117.
    The degree structure of functions induced by a polynomial-time reducibility first introduced in G. Miller's work on the complexity of prime factorization is investigated. Several basic results are established including the facts that the degrees restricted to the sets do not form an upper semilattice and there is a minimal degree, as well as density for the low degrees, a weak form of the exact pair theorem, the existence of minimal pairs and the decidability of the Π2 theory of (...)
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  28.  17
    Román Sasyk & Asger Törnquist (2009). Borel Reducibility and Classification of von Neumann Algebras. Bulletin of Symbolic Logic 15 (2):169-183.
    We announce some new results regarding the classification problem for separable von Neumann algebras. Our results are obtained by applying the notion of Borel reducibility and Hjorth's theory of turbulence to the isomorphism relation for separable von Neumann algebras.
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  29.  13
    D. A. Bočvar (1979). Measures of Kearnels of Reducibility Axioms and Singlets. Studia Logica 38 (4):393 - 400.
    The present paper is a generalization and further development of the theory of Kernel measures of reducibility axioms formulated in [1], [2], [3] in. the years 1969–1973. In this paper logical connections of Kernel measures with some set-theoretical notions are studied and some suggestions related to these connections are formulated.
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  30.  20
    Pierdaniele Giaretta (1998). Liar, Reducibility and Language. Synthese 117 (3):355-374.
    First, language and axioms of Church's paper 'Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski' are slightly modified and a version of the Liar paradox tentatively reconstructed. An obvious natural solution of the paradox leads to a hierarchy of truth predicates which is of a different kind from the one defined by Church: it depends on the enlargement of the semantical vocabulary and its levels do not differ in the ramified-type-theoretical sense. Second, two attempts are made (...)
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  31.  13
    Ernst Kleinert (2007). On the Reducibility of Relations: Variations on a Theme of Peirce. Transactions of the Charles S. Peirce Society 43 (3):509 - 520.
    : The paper presents some mathematical aspects of the question of reducibility of relations. After giving a formal definition of reducibility we present the basic result (due to Herzberger) to the effect that relations of valency at least 3 are always reducible if the cardinality of the relation is at most equal to the cardinality of the underlying set (which is automatically the case if this set is infinite). In contrast to this, if the term "reduction" is given (...)
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  32.  1
    Jean Gallier (1998). Typing Untyped Λ-Terms, or Reducibility Strikes Again! Annals of Pure and Applied Logic 91 (2-3):231-270.
    It was observed by Curry that when λ-terms can be assigned types, for example, simple types, these terms have nice properties . Coppo, Dezani, and Veneri, introduced type systems using conjunctive types, and showed that several important classes of terms can be characterized according to the shape of the types that can be assigned to these terms. For example, the strongly normalizable terms, the normalizable terms, and the terms having head-normal forms, can be characterized in some systems and Ω. The (...)
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  33.  8
    John T. Gill Iii & Paul H. Morris (1974). On Subcreative Sets and S-Reducibility. Journal of Symbolic Logic 39 (4):669 - 677.
    Subcreative sets, introduced by Blum, are known to coincide with the effectively speedable sets. Subcreative sets are shown to be the complete sets with respect to S-reducibility, a special case of Turing reducibility. Thus a set is effectively speedable exactly when it contains the solution to the halting problem in an easily decodable form. Several characterizations of subcreative sets are given, including the solution of an open problem of Blum, and are used to locate the subcreative sets with (...)
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  34.  9
    Edwin D. Mares (2007). The Fact Semantics for Ramified Type Theory and the Axiom of Reducibility. Notre Dame Journal of Formal Logic 48 (2):237-251.
    This paper uses an atomistic ontology of universals, individuals, and facts to provide a semantics for ramified type theory. It is shown that with some natural constraints on the sort of universals and facts admitted into a model, the axiom of reducibility is made valid.
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  35. Harvey Friedman, Axiomatization of Set Theory by Extensionality, Separation, and Reducibility.
    We discuss several axiomatizations of set theory in first order predicate calculus with epsilon and a constant symbol W, starting with the simple system K(W) which has a strong equivalence with ZF without Foundation. The other systems correspond to various extensions of ZF by certain large cardinal hypotheses. These axiomatizations are unusually simple and uncluttered, and are highly suggestive of underlying philosophical principles that generate higher set theory.
     
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  36. William E. Seager (2006). Rosenberg, Reducibility and Consciousness. Psyche 12.
    Rosenberg’s general argumentative strategy in favour of panpsychism is an extension of a traditional pattern. Although his argument is complex and intricate, I think a model that is historically significant and fundamentally similar to the position Rosenberg advances might help us understand the case for panpsychism. Thus I want to begin by considering a Leibnizian argument for panpsychism.
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  37. Ausonio Marras (1993). Supervenience and Reducibility: An Odd Couple. Philosophical Quarterly 44 (171):215-222.
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  38.  8
    S. Cooper & Mariya Soskova (2008). How Enumeration Reducibility Yields Extended Harrington Non-Splitting. Journal of Symbolic Logic 73 (2):634-655.
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  39.  17
    Clark Butler (1995). The Reducibility of Ethics to Human Rights. Dialogue and Universalism 7.
    First Statement of what would become Human Rights Ethics, Purdue University Press, 2008.
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  40.  93
    Philip Nochlin (1953). Reducibility and Intentional Words. Journal of Philosophy 50 (October):625-637.
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  41.  4
    Richard M. Friedberg & Hartley Rogers (1959). Reducibility and Completeness for Sets of Integers. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5 (7-13):117-125.
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  42. I. L. Humberstone (1995). Comparatives and the Reducibility of Relations. Pacific Philosophical Quarterly 76 (2):117-141.
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  43.  25
    Edward L. Keenan (1993). Natural Language, Sortal Reducibility and Generalized Quantifiers. Journal of Symbolic Logic 58 (1):314-325.
    Recent work in natural language semantics leads to some new observations on generalized quantifiers. In § 1 we show that English quantifiers of type $ $ are booleanly generated by their generalized universal and generalized existential members. These two classes also constitute the sortally reducible members of this type. Section 2 presents our main result--the Generalized Prefix Theorem (GPT). This theorem characterizes the conditions under which formulas of the form Q1x 1⋯ Qnx nRx 1⋯ xn and q1x 1⋯ qnx nRx (...)
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  44.  5
    Caterina Bianchini & Andrea Sorbi (1992). Reducibility in Some Categories of Partial Recursive Operators. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):349-359.
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  45.  2
    Richard M. Friedberg & Hartley Rogers (1959). Reducibility and Completeness for Sets of Integers. Mathematical Logic Quarterly 5 (7‐13):117-125.
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  46.  21
    Harold Kincaid (1987). Supervenience Doesn't Entail Reducibility. Southern Journal of Philosophy 25 (3):343-56.
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  47.  2
    Mariya I. Soskova & S. Barry Cooper (2008). How Enumeration Reducibility Yields Extended Harrington Non-Splitting. Journal of Symbolic Logic 73 (2):634 - 655.
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  48.  4
    A. H. Lachlan (1965). Some Notions of Reducibility and Productiveness. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 11 (1):17-44.
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  49.  4
    S. Barry Cooper (1987). Enumeration Reducibility Using Bounded Information: Counting Minimal Covers. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (6):537-560.
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  50.  4
    Karol Habart & K. Habart (1992). Bounds in the Turing Reducibility of Functions. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):423-430.
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