Results for 'Strong minimal cover'

973 found
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  1.  16
    Strong Minimal Covers for Recursively Enumerable Degrees.S. Barry Cooper - 1996 - Mathematical Logic Quarterly 42 (1):191-196.
    We prove that there exists a nonzero recursively enumerable Turing degree possessing a strong minimal cover.
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  2.  11
    Strong Minimal Covers for Recursively Enumerable Degrees.S. Cooper - 1996 - Mathematical Logic Quarterly 42 (1):191-196.
    We prove that there exists a nonzero recursively enumerable Turing degree possessing a strong minimal cover.
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  3. A 1-generic degree with a strong minimal cover.Masahiro Kumabe - 2000 - Journal of Symbolic Logic 65 (3):1395-1442.
  4.  54
    DMP in Strongly Minimal Sets.Assaf Hasson & Ehud Hrushovski - 2007 - Journal of Symbolic Logic 72 (3):1019 - 1030.
    We construct a strongly minimal set which is not a finite cover of one with DMP. We also show that for a strongly minimal theory T, generic automorphisms exist iff T has DMP, thus proving a conjecture of Kikyo and Pillay.
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  5. Minimal inconsistency-tolerant logics: a quantitative approach.Christian Strasser & Sanderson Molick - 2025 - Australasian Journal of Logic 22 (03):308-365.
    In order to reason in a non-trivializing way with contradictions, para- consistent logics reject some classically valid inferences. As a way of re- covering some of these inferences, Graham Priest ([Priest, 1991]) proposed to nonmonotonically strengthen the Logic of Paradox by allowing the se- lection of “less inconsistent” models via a comparison of their respective inconsistent parts. This move recaptures a good portion of classical logic in that it does not block, e.g., disjunctive syllogism, unless it is applied to contradictory (...)
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  6.  26
    Computability and the Symmetric Difference Operator.Uri Andrews, Peter M. Gerdes, Steffen Lempp, Joseph S. Miller & Noah D. Schweber - 2022 - Logic Journal of the IGPL 30 (3):499-518.
    Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.
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  7.  31
    On isomorphism classes of computably enumerable equivalence relations.Uri Andrews & Serikzhan A. Badaev - 2020 - Journal of Symbolic Logic 85 (1):61-86.
    We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete ceers contained in the (...)
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  8.  38
    On the Structure of Computable Reducibility on Equivalence Relations of Natural Numbers.Uri Andrews, Daniel F. Belin & Luca San Mauro - 2023 - Journal of Symbolic Logic 88 (3):1038-1063.
    We examine the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ of equivalence relations on $\omega $ under computable reducibility. We examine when pairs of degrees have a least upper bound. In particular, we show that sufficiently incomparable pairs of degrees do not have a least upper bound but that some incomparable degrees do, and we characterize the degrees which have a least upper bound with every finite equivalence relation. We show that the natural classes of finite, light, and dark degrees are (...)
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  9.  65
    Array nonrecursiveness and relative recursive enumerability.Mingzhong Cai - 2012 - Journal of Symbolic Logic 77 (1):21-32.
    In this paper we prove that a degree a is array nonrecursive (ANR) if and only if every degree b ≥ a is r.e. in and strictly above another degree (RRE). This result will answer some questions in [ASDWY]. We also deduce an interesting corollary that every n-REA degree has a strong minimal cover if and only if it is array recursive.
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  10.  61
    Intervals containing exactly one c.e. degree.Guohua Wu - 2007 - Annals of Pure and Applied Logic 146 (1):91-102.
    Cooper proved in [S.B. Cooper, Strong minimal covers for recursively enumerable degrees, Math. Logic Quart. 42 191–196] the existence of a c.e. degree with a strong minimal cover . So is the greastest c.e. degree below . Cooper and Yi pointed out in [S.B. Cooper, X. Yi, Isolated d.r.e. degrees, University of Leeds, Dept. of Pure Math., 1995. Preprint] that this strongly minimal cover cannot be d.c.e., and meanwhile, they proposed the notion of (...)
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  11.  25
    Initial Segments of the Degrees of Ceers.Uri Andrews & Andrea Sorbi - 2022 - Journal of Symbolic Logic 87 (3):1260-1282.
    It is known that every non-universal self-full degree in the structure of the degrees of computably enumerable equivalence relations (ceers) under computable reducibility has exactly one strong minimal cover. This leaves little room for embedding wide partial orders as initial segments using self-full degrees. We show that considerably more can be done by staying entirely inside the collection of non-self-full degrees. We show that the poset can be embedded as an initial segment of the degrees of ceers (...)
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  12.  40
    The definable multiplicity property and generic automorphisms.Hirotaka Kikyo & Anand Pillay - 2000 - Annals of Pure and Applied Logic 106 (1-3):263-273.
    Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T{“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T{“σi is an (...)
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  13.  67
    Decision procedures for some strong hybrid logics.Andrzej Indrzejczak & Michał Zawidzki - 2013 - Logic and Logical Philosophy 22 (4):389-409.
    Hybrid logics are extensions of standard modal logics, which significantly increase the expressive power of the latter. Since most of hybrid logics are known to be decidable, decision procedures for them is a widely investigated field of research. So far, several tableau calculi for hybrid logics have been presented in the literature. In this paper we introduce a sound, complete and terminating tableau calculus T H(@,E,D, ♦ −) for hybrid logics with the satisfaction operators, the universal modality, the difference modality (...)
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  14.  43
    On the Symmetric Enumeration Degrees.Charles M. Harris - 2007 - Notre Dame Journal of Formal Logic 48 (2):175-204.
    A set A is symmetric enumeration (se-) reducible to a set B (A ≤\sb se B) if A is enumeration reducible to B and \barA is enumeration reducible to \barB. This reducibility gives rise to a degree structure (D\sb se) whose least element is the class of computable sets. We give a classification of ≤\sb se in terms of other standard reducibilities and we show that the natural embedding of the Turing degrees (D\sb T) into the enumeration degrees (D\sb e) (...)
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  15.  20
    Strongly Minimal Reducts of Valued Fields.Piotr Kowalski & Serge Randriambololona - 2016 - Journal of Symbolic Logic 81 (2):510-523.
    We prove that if a strongly minimal nonlocally modular reduct of an algebraically closed valued field of characteristic 0 contains +, then this reduct is bi-interpretable with the underlying field.
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  16.  57
    Automorphism groups of trivial strongly minimal structures.Thomas Blossier - 2003 - Journal of Symbolic Logic 68 (2):644-668.
    We study automorphism groups of trivial strongly minimal structures. First we give a characterization of structures of bounded valency through their groups of automorphisms. Then we characterize the triplets of groups which can be realized as the automorphism group of a non algebraic component, the subgroup stabilizer of a point and the subgroup of strong automorphisms in a trivial strongly minimal structure, and also we give a reconstruction result. Finally, using HNN extensions we show that any profinite (...)
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  17.  25
    Strongly minimal Steiner systems I: Existence.John Baldwin & Gianluca Paolini - 2021 - Journal of Symbolic Logic 86 (4):1486-1507.
    A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner k-system is a linear space such that each line has size exactly k. Clearly, as a two-sorted structure, no linear space can be strongly minimal. We formulate linear spaces in a vocabulary $\tau $ with a single ternary relation R. We prove that for every integer k there exist $2^{\aleph _0}$ -many integer valued functions $\mu $ such (...)
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  18. Pseudoprojective strongly minimal sets are locally projective.Steven Buechler - 1991 - Journal of Symbolic Logic 56 (4):1184-1194.
    Let D be a strongly minimal set in the language L, and $D' \supset D$ an elementary extension with infinite dimension over D. Add to L a unary predicate symbol D and let T' be the theory of the structure (D', D), where D interprets the predicate D. It is known that T' is ω-stable. We prove Theorem A. If D is not locally modular, then T' has Morley rank ω. We say that a strongly minimal set D (...)
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  19.  75
    Local Homogeneity.Bektur Baizhanov & John T. Baldwin - 2004 - Journal of Symbolic Logic 69 (4):1243 - 1260.
    We study the expansion of stable structures by adding predicates for arbitrary subsets. Generalizing work of Poizat-Bouscaren on the one hand and Baldwin-Benedikt-Casanovas-Ziegler on the other we provide a sufficient condition (Theorem 4.7) for such an expansion to be stable. This generalization weakens the original definitions in two ways: dealing with arbitrary subsets rather than just submodels and removing the 'small' or 'belles paires' hypothesis. We use this generalization to characterize in terms of pairs, the 'triviality' of the geometry on (...)
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  20.  31
    Strongly minimal fusions of vector spaces.Kitty L. Holland - 1997 - Annals of Pure and Applied Logic 83 (1):1-22.
    We provide a simple and transparent construction of Hrushovski's strongly minimal fusions in the case where the fused strongly minimal sets are vector spaces. We strengthen Hrushovski's result by showing that the strongly minimal fusions are model complete.
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  21.  93
    On strongly minimal sets.J. T. Baldwin & A. H. Lachlan - 1971 - Journal of Symbolic Logic 36 (1):79-96.
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  22.  69
    Strongly Minimal Groups in the Theory of Compact Complex Spaces.Matthias Aschenbrenner, Rahim Moosa & Thomas Scanlon - 2006 - Journal of Symbolic Logic 71 (2):529 - 552.
    We characterise strongly minimal groups interpretable in elementary extensions of compact complex analytic spaces.
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  23.  14
    Ax-Schanuel and strong minimality for the j-function.Vahagn Aslanyan - 2021 - Annals of Pure and Applied Logic 172 (1):102871.
  24.  26
    On the minimal cover property and certain notions of finite.Eleftherios Tachtsis - 2018 - Archive for Mathematical Logic 57 (5-6):665-686.
    In set theory without the axiom of choice, we investigate the deductive strength of the principle “every topological space with the minimal cover property is compact”, and its relationship with certain notions of finite as well as with properties of linearly ordered sets and partially ordered sets.
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  25.  33
    New spectra of strongly minimal theories in finite languages.Uri Andrews - 2011 - Annals of Pure and Applied Logic 162 (5):367-372.
    We describe strongly minimal theories Tn with finite languages such that in the chain of countable models of Tn, only the first n models have recursive presentations. Also, we describe a strongly minimal theory with a finite language such that every non-saturated model has a recursive presentation.
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  26.  29
    A strongly minimal expansion of (ω, s).David Marker - 1987 - Journal of Symbolic Logic 52 (1):205-207.
  27.  18
    Strong minimal pairs in the enumeration degrees.Josiah Jacobsen-Grocott - 2024 - Annals of Pure and Applied Logic 175 (10):103464.
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  28. Strongly minimal group relics of algebraically closed valued fields.Assaf Hasson, Alf Onshuus & Santiago Pinzon - forthcoming - Journal of Mathematical Logic.
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  29. Almost strongly minimal theories. I.John T. Baldwin - 1972 - Journal of Symbolic Logic 37 (3):487-493.
  30.  61
    Minimal Risk in Research Involving Pregnant Women and Fetuses.Carson Strong - 2011 - Journal of Law, Medicine and Ethics 39 (3):529-538.
    How should the definition of “minimal risk” in the federal research regulations be interpreted in regard to pregnant women and fetuses? Surprisingly, there has been little discussion of this question. There is, after all, a substantial amount of published work addressing the question of how “minimal risk” should be interpreted. Similarly, there is a large body of literature on the ethics of research involving pregnant women and fetuses, particularly maternal-fetal surgery. However, in neither of these bodies of work (...)
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  31.  68
    A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
    We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties.
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  32. Almost strongly minimal theories. II.John T. Baldwin - 1972 - Journal of Symbolic Logic 37 (4):657-660.
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  33.  89
    Finitely axiomatizable strongly minimal groups.Thomas Blossier & Elisabeth Bouscaren - 2010 - Journal of Symbolic Logic 75 (1):25-50.
    We show that if G is a strongly minimal finitely axiomatizable group, the division ring of quasi-endomorphisms of G must be an infinite finitely presented ring.
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  34.  59
    Strongly and co-strongly minimal abelian structures.Ehud Hrushovski & James Loveys - 2010 - Journal of Symbolic Logic 75 (2):442-458.
    We give several characterizations of weakly minimal abelian structures. In two special cases, dual in a sense to be made explicit below, we give precise structure theorems: 1. When the only finite 0-definable subgroup is {0}, or equivalently 0 is the only algebraic element (the co-strongly minimal case); 2. When the theory of the structure is strongly minimal. In the first case, we identify the abelian structure as a "near-subspace" A of a vector space V over a (...)
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  35.  32
    Computable Embeddings and Strongly Minimal Theories.J. Chisholm, J. F. Knight & S. Miller - 2007 - Journal of Symbolic Logic 72 (3):1031 - 1040.
    Here we prove that if T and T′ are strongly minimal theories, where T′ satisfies a certain property related to triviality and T does not, and T′ is model complete, then there is no computable embedding of Mod(T) into Mod(T′). Using this, we answer a question from [4], showing that there is no computable embedding of VS into ZS, where VS is the class of infinite vector spaces over Q, and ZS is the class of models of Th(Z, S). (...)
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  36.  95
    Minimal but not strongly minimal structures with arbitrary finite dimensions.Koichiro Ikeda - 2001 - Journal of Symbolic Logic 66 (1):117-126.
    An infinite structure is said to be minimal if each of its definable subset is finite or cofinite. Modifying Hrushovski's method we construct minimal, non strongly minimal structures with arbitrary finite dimensions. This answers negatively to a problem posed by B. I Zilber.
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  37.  20
    Interpreting groups inside modular strongly minimal homogeneous models.Tapani Hyttinen - 2003 - Journal of Mathematical Logic 3 (01):127-142.
    A large homogeneous model M is strongly minimal, if any definable subset is either bounded or has bounded complement. In this case is a pregeometry, where bcl denotes the bounded closure operation. In this paper, we show that if M is a large homogeneous strongly minimal structure and is non-trivial and locally modular, then M interprets a group. In addition, we give a description of such groups.
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  38.  59
    Genomic Sexuality and Self: the Cultural Conditions for the “Uptake” of Gay Gene Assertions.Rob Cover - 2010 - Dialogue and Universalism 20 (5-6):59-76.
    Many areas of genetic research, genetic forensics and genetic essentialism are treated in public sphere debate as suspicious and problematic or are subject to waves of moral panic. In cultural theory, likewise, strong critiques of the genetic essentialism emerge as part of a broader critical assessment of the discourses of the biological sciences and the assertion of a connection between genes and human behavior. However, the scientific and popular claim to the existence of a “gay gene” is not treated (...)
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  39.  45
    Ehud Hrushovski, A new strongly minimal set, Annals of pure and applied logic, vol. 62 , pp. 147–166. - Ehud Hrushovski, Strongly minimal expansions of algebraically closed fields, Israel journal of mathematics, vol. 79 , pp. 129–151. [REVIEW]John Baldwin - 1999 - Journal of Symbolic Logic 64 (2):904-905.
  40.  51
    Non Σn axiomatizable almost strongly minimal theories.David Marker - 1989 - Journal of Symbolic Logic 54 (3):921 - 927.
  41.  60
    The geometry of Hrushovski constructions, II. The strongly minimal case.David M. Evans & Marco S. Ferreira - 2012 - Journal of Symbolic Logic 77 (1):337-349.
    We investigate the isomorphism types of combinatorial geometries arising from Hrushovski's flat strongly minimal structures and answer some questions from Hrushovski's original paper.
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  42.  9
    Geometric triviality of the strongly minimal second Painlevé equations.Joel Nagloo - 2015 - Annals of Pure and Applied Logic 166 (3):358-368.
  43.  61
    B. I. Zil′ber. Totally categorical theories: structural properties and the non-finite axiomatizability. Model theory of algebra and arithmetic, Proceedings of the conference on applications of logic to algebra and arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 381–410. - B. I. Zil′ber. Strongly minimal countably categorical theories. Siberian mathematical journal, vol. 21 no. 2 , pp. 219–230. , pp. 98-112.) - B. I. Zil′ber. Strongly minimal countably categorical theories. II. Ibid., vol. 25 no. 3 , pp. 396-412. , pp. 71-88.) - B. I. Zil′ber. Strongly minimal countably categorical theories. III. Ibid., vol. 25 no. 4 , pp. 559-571. , pp. 63-77.) - B. I. Zil′ber. Totally categorical structures and combinatorial geometries. Soviet mathematics–Doklady, vol. 24 no. 1 , pp. 149-151. , pp. 1039-1041.) - B. I. Zil′ber The struc. [REVIEW]Ehud Hrushovski - 1993 - Journal of Symbolic Logic 58 (2):710-713.
    Reviewed Works:B. I. Zil'ber, L. Pacholski, J. Wierzejewski, A. J. Wilkie, Totally Categorical Theories: Structural Properties and the Non-Finite Axiomatizability.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. II.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. III.B. I. Zil'ber, E. Mendelson, Totally Categorical Structures and Combinatorial Geometries.B. I. Zil'ber, The Structure of Models of Uncountably Categorical Theories.
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  44.  42
    An exposition of Hrushovskiʼs New Strongly Minimal Set.Martin Ziegler - 2013 - Annals of Pure and Applied Logic 164 (12):1507-1519.
    We give an exposition of Hrushovskiʼs New Strongly Minimal Set : A strongly minimal theory which is not locally modular but does not interpret an infinite field. We give an exposition of his construction.
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  45.  93
    On the existence of a strong minimal pair.George Barmpalias, Mingzhong Cai, Steffen Lempp & Theodore A. Slaman - 2015 - Journal of Mathematical Logic 15 (1):1550003.
    We show that there is a strong minimal pair in the computably enumerable Turing degrees, i.e. a pair of nonzero c.e. degrees a and b such that a∩b = 0 and for any nonzero c.e. degree x ≤ a, b ∪ x ≥ a.
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  46.  23
    Is a spectrum of a non-disintegrated flat strongly minimal model complete theory in a language with finite signature.Uri Andrews & Omer Mermelstein - 2021 - Journal of Symbolic Logic 86 (4):1632-1656.
    We build a new spectrum of recursive models (SRM(T)) of a strongly minimal theory. This theory is non-disintegrated, flat, model complete, and in a language with a finite structure.
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  47.  17
    Interpreting structures of finite Morley rank in strongly minimal sets.Assaf Hasson - 2007 - Annals of Pure and Applied Logic 145 (1):96-114.
    We show that any structure of finite Morley Rank having the definable multiplicity property has a rank and multiplicity preserving interpretation in a strongly minimal set. In particular, every totally categorical theory admits such an interpretation. We also show that a slightly weaker version of the DMP is necessary for a structure of finite rank to have a strongly minimal expansion. We conclude by constructing an almost strongly minimal set which does not have the DMP in any (...)
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  48. One theorem of Zil′ber's on strongly minimal sets.Steven Buechler - 1985 - Journal of Symbolic Logic 50 (4):1054-1061.
    Suppose $D \subset M$ is a strongly minimal set definable in M with parameters from C. We say D is locally modular if for all $X, Y \subset D$ , with $X = \operatorname{acl}(X \cup C) \cap D, Y = \operatorname{acl}(Y \cup C) \cap D$ and $X \cap Y \neq \varnothing$ , dim(X ∪ Y) + dim(X ∩ Y) = dim(X) + dim(Y). We prove the following theorems. Theorem 1. Suppose M is stable and $D \subset M$ is strongly (...)
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  49.  20
    (1 other version)Enumeration Reducibility Using Bounded Information: Counting Minimal Covers.S. Barry Cooper - 1987 - Mathematical Logic Quarterly 33 (6):537-560.
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  50.  82
    Pseudo-Jump Operators. II: Transfinite Iterations, Hierarchies and Minimal Covers.Carl G. Jockusch & Richard A. Shore - 1984 - Journal of Symbolic Logic 49 (4):1205 - 1236.
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