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489The ibT degrees of computably enumerable sets are not denseAnnals of Pure and Applied Logic 141 (1): 51-60. 2006.We show that the identity bounded Turing degrees of computably enumerable sets are not dense
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115A C.E. Real That Cannot Be SW-Computed by Any Ω NumberNotre Dame Journal of Formal Logic 47 (2): 197-209. 2006.The strong weak truth table (sw) reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occurs naturally in proofs in classical computability theory as well as in the recent work of Soare, Nabutovsky, and Weinberger on applications of computability to differential geometry. We study the sw-degrees of c.e. reals and construct a c.e. real which has no random c.e. real (i.e., Ω number) sw-above it
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83The importance of Π1 0 classes in effective randomnessJournal of Symbolic Logic 75 (1): 387-400. 2010.We prove a number of results in effective randomness, using methods in which Π⁰₁ classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.
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79A call for an expanded synthesis of developmental and evolutionary paradigmsBehavioral and Brain Sciences 35 (5): 368-369. 2012.Charney's target article continues a critique of genetic blueprint models of development that suggests reconsideration of concepts of adaptation, inheritance, and environment, which can be well illustrated in current research on infant attachment. The concepts of development and adaptation are so heavily based on the model of genetics and inheritance forged in the modern synthesis that they will require reconsideration to accommodate epigenetic inheritance
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75The Hypersimple-Free C.E. WTT Degrees Are Dense in the C.E. WTT DegreesNotre Dame Journal of Formal Logic 47 (3): 361-370. 2006.We show that in the c.e. weak truth table degrees if b < c then there is an a which contains no hypersimple set and b < a < c. We also show that for every w < c in the c.e. wtt degrees such that w is hypersimple, there is a hypersimple a such that w < a < c. On the other hand, we know that there are intervals which contain no hypersimple set
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67Empty intervals in the enumeration degreesAnnals of Pure and Applied Logic 163 (5): 567-574. 2012.
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56Topological aspects of the Medvedev latticeArchive for Mathematical Logic 50 (3-4): 319-340. 2011.We study the Medvedev degrees of mass problems with distinguished topological properties, such as denseness, closedness, or discreteness. We investigate the sublattices generated by these degrees; the prime ideal generated by the dense degrees and its complement, a prime filter; the filter generated by the nonzero closed degrees and the filter generated by the nonzero discrete degrees. We give a complete picture of the relationships of inclusion holding between these sublattices, these filters, …Read more
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50Disorganized attachment and reproductive strategiesBehavioral and Brain Sciences 32 (1): 35-36. 2009.Del Giudice provides an extension of the life history theory of attachment that incorporates emerging data suggestive of sex differences in avoidant male and preoccupied female attachment patterns emerging in middle childhood. This commentary considers the place of disorganized attachment within this theory and why male children may be more prone to disorganized attachment by drawing on Trivers's parental investment theory
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44Π 1 0 classes, L R degrees and Turing degreesAnnals of Pure and Applied Logic 156 (1): 21-38. 2008.We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study this relation and its interactions with Turing reducibility, classes, hyperimmunity and other recursion theoretic notions.
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41Randomness and the linear degrees of computabilityAnnals of Pure and Applied Logic 145 (3): 252-257. 2007.We show that there exists a real α such that, for all reals β, if α is linear reducible to β then β≤Tα. In fact, every random real satisfies this quasi-maximality property. As a corollary we may conclude that there exists no ℓ-complete Δ2 real. Upon realizing that quasi-maximality does not characterize the random reals–there exist reals which are not random but which are of quasi-maximal ℓ-degree–it is then natural to ask whether maximality could provide such a characterization. Such hopes, howe…Read more
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40Randomness, Lowness and DegreesJournal of Symbolic Logic 73 (2). 2008.We say that A ≤LR B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real γ. In other words. B is at least as good as A for this purpose. We study the structure of the LR degrees globally and locally (i.e., restricted to the computably enumberable degrees) and their relationship with the Turing degrees. Among other results we show that whenever α in not GL₂ the LR degree of α bounds $2^{\aleph _{0}}$ degrees (so that, in particular,…Read more
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31Diagonally non-computable functions and bi-immunityJournal of Symbolic Logic 78 (3): 977-988. 2013.
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152008 Annual Meeting of the Association for Symbolic Logic-University of California, Irvine-Irvine, California-March 27-30, 2008-Abstracts (review)Bulletin of Symbolic Logic 14 (3): 418-437. 2008.
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2The Role of Supervision in the Training of a PsychoanalystAnalysis (Australian Centre for Psychoanalysis) 13 85. 2007.
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The importance of $\Pi _1^0$ classes in effective randomness. The Journal of Symbolic Logic, vol. 75Bulletin of Symbolic Logic 18 (3): 409-412. 2012.
