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Automorphisms of the lattice of recursively enumerable sets: Orbits, Adv
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Cited by 32 (15 self)
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JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. American Mathematical Society is collaborating with JSTOR to digitize, preserve and extend access to
Bounded Immunity and BttReductions
 MLQ Math. Log. Q
, 1999
"... We define and study a new notion called kimmunity that lies between immunity and hyperimmunity in strength. Our interest in kimmunity is justified by the result that # # does not ktt reduce to a kimmune set, which improves a previous result by Kobzev [7, 13]. We apply the result to show that ..."
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Cited by 7 (3 self)
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We define and study a new notion called kimmunity that lies between immunity and hyperimmunity in strength. Our interest in kimmunity is justified by the result that # # does not ktt reduce to a kimmune set, which improves a previous result by Kobzev [7, 13]. We apply the result to show that # # does not bttreduce to MIN, the set of minimal programs. Other applications include the set of Kolmogorov random strings, and retraceable and regressive sets. We also give a new characterization of e#ectively simple sets and show that simple sets are not bttcuppable. Keywords: Computability, Recursion Theory, bounded reducibilities, minimal programs, immunity, kimmune, regressive, retraceable, e#ectively simple, cuppable. 1 Introduction There seems to be a large gap between immunity and hyperimmunity (himmunity) that is waiting to be filled. What happens, one wonders if the disjoint strong arrays that try to witness that a set is not himmune are subjected to additional conditions...
Needed Reals and Recursion in Generic Reals \Lambda
"... We shall be interested in triples A = (A\Gamma; A+; A) where A is a binary relation between the sets A\Gamma and A+. We often call such triples "relations. " Call a subset X ` A+ adequate for A if ..."
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We shall be interested in triples A = (A\Gamma; A+; A) where A is a binary relation between the sets A\Gamma and A+. We often call such triples "relations. " Call a subset X ` A+ adequate for A if
A Note on a Variant of Immunity, BttReducibility, and Minimal Programs
, 1996
"... We define and study a new notion called kimmunity that lies between immunity and hyperimmunity in strength. Our interest in kimmunity is justified by the result that K does not ktt reduce to a kimmune set which improves a previous result by Kobzev [6]. We apply the result to show that K does ..."
Abstract
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We define and study a new notion called kimmunity that lies between immunity and hyperimmunity in strength. Our interest in kimmunity is justified by the result that K does not ktt reduce to a kimmune set which improves a previous result by Kobzev [6]. We apply the result to show that K does not bttreduce to MIN, the set of minimal programs. Other applications include the set of Kolmogorov random strings, and retraceable and regressive sets. We also give a new characterization of effectively simple sets, and add some results about regressive sets. Keywords: Computability, bounded reducibilities, minimal programs, immunity. 1
965 AGENDA
"... this article, we retrace the history of computability theory since 1965 in relation to the questions raised by Rogers, and try to shed a little more light on those for which solutions have yet to appear ..."
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this article, we retrace the history of computability theory since 1965 in relation to the questions raised by Rogers, and try to shed a little more light on those for which solutions have yet to appear
Relativization of the Theory of Computational Complexity
, 1976
"... The axiomatic treatment of the computational complexity of partial recurslye functions initiated by Blum is extended to relatively com putable functions (as computed, for example, by Turing machines with oracles). ..."
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The axiomatic treatment of the computational complexity of partial recurslye functions initiated by Blum is extended to relatively com putable functions (as computed, for example, by Turing machines with oracles).
STRONG DEGREE SPECTRA OF RELATIONS
, 2008
"... For my husband Andrew, and children Prudence, Jancis, and Rutherford. One of the main areas of study in computable model theory is examining how certain aspects of a computable structure may change under an isomorphism to another computable structure. Let A be a computable structure, and let R be an ..."
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For my husband Andrew, and children Prudence, Jancis, and Rutherford. One of the main areas of study in computable model theory is examining how certain aspects of a computable structure may change under an isomorphism to another computable structure. Let A be a computable structure, and let R be an additional relation on the domain of A, so it is not named in the language of A. Harizanov defined the Turing degree spectrum of R on A to be the set of all Turing degrees of the images of R under all isomorphisms from A onto computable structures. Similarly, we define this notion for strong degrees such as weak truthtable degrees and truthtable degrees. We show that the conditions necessary for the Turing degree spectrum to contain all Turing degrees, found by Harizanov, are also enough to have the truthtable degree spectrum to contain all truthtable degrees. We further study the degreetheoretic complexity of initial segments of computable linear orderings. In particular, let L be a computable linear ordering of order type ω+ω ∗. Harizanov showed that the Turing degree spectrum of the ωpart of L is all of the limit computable