Results for 'Peter A. Cholak'

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  1.  11
    Corrigendum to: "On the Strength of Ramsey's Theorem for Pairs".Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2009 - Journal of Symbolic Logic 74 (4):1438 - 1439.
  2. On the strength of Ramsey's theorem for pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
    We study the proof-theoretic strength and effective content of the infinite form of Ramsey's theorem for pairs. Let RT n k denote Ramsey's theorem for k-colorings of n-element sets, and let RT $^n_{ denote (∀ k)RT n k . Our main result on computability is: For any n ≥ 2 and any computable (recursive) k-coloring of the n-element sets of natural numbers, there is an infinite homogeneous set X with X'' ≤ T 0 (n) . Let IΣ n and BΣ (...)
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  3.  55
    On the definability of the double jump in the computably enumerable sets.Peter A. Cholak & Leo A. Harrington - 2002 - Journal of Mathematical Logic 2 (02):261-296.
    We show that the double jump is definable in the computably enumerable sets. Our main result is as follows: let [Formula: see text] is the Turing degree of a [Formula: see text] set J ≥T0″}. Let [Formula: see text] such that [Formula: see text] is upward closed in [Formula: see text]. Then there is an ℒ property [Formula: see text] such that [Formula: see text] if and only if there is an A where A ≡T F and [Formula: see text]. (...)
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  4.  16
    On Mathias generic sets.Peter A. Cholak, Damir D. Dzhafarov & Jeffry L. Hirst - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 129--138.
  5.  14
    On n -tardy sets.Peter A. Cholak, Peter M. Gerdes & Karen Lange - 2012 - Annals of Pure and Applied Logic 163 (9):1252-1270.
  6.  62
    Definable encodings in the computably enumerable sets.Peter A. Cholak & Leo A. Harrington - 2000 - Bulletin of Symbolic Logic 6 (2):185-196.
    The purpose of this communication is to announce some recent results on the computably enumerable sets. There are two disjoint sets of results; the first involves invariant classes and the second involves automorphisms of the computably enumerable sets. What these results have in common is that the guts of the proofs of these theorems uses a new form of definable coding for the computably enumerable sets.We will work in the structure of the computably enumerable sets. The language is just inclusion, (...)
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  7.  72
    The complexity of orbits of computably enumerable sets.Peter A. Cholak, Rodney Downey & Leo A. Harrington - 2008 - Bulletin of Symbolic Logic 14 (1):69 - 87.
    The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...)
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  8.  68
    Iterated relative recursive enumerability.Peter A. Cholak & Peter G. Hinman - 1994 - 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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  9.  42
    Isomorphisms of splits of computably enumerable sets.Peter A. Cholak & Leo A. Harrington - 2003 - Journal of Symbolic Logic 68 (3):1044-1064.
    We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.
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  10.  22
    ${\Cal d}$-maximal sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
    Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal (...)
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  11.  21
    -Maximal sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
    Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal (...)
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  12.  15
    Participants and titles of lectures.Klaus Ambos-Spies, Marat Arslanov, Douglas Cenzer, Peter Cholak, Chi Tat Chong, Decheng Ding, Rod Downey, Peter A. Fejer, Sergei S. Goncharov & Edward R. Griffor - 1998 - Annals of Pure and Applied Logic 94 (1):3-6.
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  13.  60
    Computably categorical structures and expansions by constants.Peter Cholak, Sergey Goncharov, Bakhadyr Khoussainov & Richard A. Shore - 1999 - Journal of Symbolic Logic 64 (1):13-37.
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  14.  11
    Corrigendum to: “On the strength of Ramsey's Theorem for pairs”.Peter Cholak, Jr} {Jockusch & Theodore A. Slaman - 2009 - Journal of Symbolic Logic 74 (4):1438-1439.
  15. A computably stable structure with no Scott family of finitary formulas.Peter Cholak, Richard A. Shore & Reed Solomon - 2006 - Archive for Mathematical Logic 45 (5):519-538.
  16.  63
    Uniform Almost Everywhere Domination.Peter Cholak, Noam Greenberg & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (3):1057 - 1072.
    We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.
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  17.  65
    An almost deep degree.Peter Cholak, Marcia Groszek & Theodore Slaman - 2001 - Journal of Symbolic Logic 66 (2):881-901.
    We show there is a non-recursive r.e. set A such that if W is any low r.e. set, then the join W $\oplus$ A is also low. That is, A is "almost deep". This answers a question of Jockusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.).
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  18.  40
    On the Cantor-bendixon rank of recursively enumerable sets.Peter Cholak & Rod Downey - 1993 - Journal of Symbolic Logic 58 (2):629-640.
    The main result of this paper is to show that for every recursive ordinal α ≠ 0 and for every nonrecursive r.e. degree d there is a r.e. set of rank α and degree d.
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  19.  47
    The translation theorem.Peter Cholak - 1994 - Archive for Mathematical Logic 33 (2):87-108.
    We state and prove the Translation Theorem. Then we apply the Translation Theorem to Soare's Extension Theorem, weakening slightly the hypothesis to yield a theorem we call the Modified Extension Theorem. We use this theorem to reprove several of the known results about orbits in the lattice of recursively enumerable sets. It is hoped that these proofs are easier to understand than the old proofs.
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  20.  36
    Some orbits for E.Peter Cholak, Rod Downey & Eberhard Herrmann - 2001 - Annals of Pure and Applied Logic 107 (1-3):193-226.
    In this article we establish the existence of a number of new orbits in the automorphism group of the computably enumerable sets. The degree theoretical aspects of these orbits also are examined.
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  21.  19
    Lattice nonembeddings and intervals of the recursively enumerable degrees.Peter Cholak & Rod Downey - 1993 - Annals of Pure and Applied Logic 61 (3):195-221.
    Let b and c be r.e. Turing degrees such that b>c. We show that there is an r.e. degree a such that b>a>c and all lattices containing a critical triple, including the lattice M5, cannot be embedded into the interval [c, a].
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  22.  52
    Maximal contiguous degrees.Peter Cholak, Rod Downey & Stephen Walk - 2002 - Journal of Symbolic Logic 67 (1):409-437.
    A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the (...)
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  23. Chapter Nineteen Evolutionary Genius and the Intensity of Artistic Life: Who Makes Musical History? Peter A. Kulichkin.Peter A. Kulichkin - 2007 - In Leonid Dorfman, Colin Martindale & Vladimir Petrov (eds.), Aesthetics and innovation. Newcastle, UK: Cambridge Scholars Press. pp. 363.
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  24.  23
    The Neurostructure of Morality and the Hubris of Memory Manipulation.I. I. Peter A. DePergola - 2018 - The New Bioethics 24 (3):199-227.
    Neurotechnologies that promise to dampen (via pharmacologicals), disassociate (via electro-convulsive therapy), erase (via deep brain stimulation), and replace (via false memory creation) unsavory episodic memories are no longer the subject of science fiction. They have already arrived, and their funding suggests that they will not disappear anytime soon. In light of their emergence, this essay examines the neurostructure of normative morality to clarify that memory manipulation, which promises to take away that which is bad in human experience, also removes that (...)
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  25.  21
    The Neurostructure of Morality and the Hubris of Memory Manipulation.I. I. Peter A. DePergola - 2018 - The New Bioethics 24 (3):199-227.
    Neurotechnologies that promise to dampen (via pharmacologicals), disassociate (via electro-convulsive therapy), erase (via deep brain stimulation), and replace (via false memory creation) unsavory episodic memories are no longer the subject of science fiction. They have already arrived, and their funding suggests that they will not disappear anytime soon. In light of their emergence, this essay examines the neurostructure of normative morality to clarify that memory manipulation, which promises to take away that which is bad in human experience, also removes that (...)
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  26.  17
    Think critically.Peter A. Facione - 2014 - Boston: Pearson. Edited by Carol Ann Gittens.
    THINK Currency. THINK Relevancy. THINK Critically. THINK Critically is a cutting-edge, self-reflective guide for improving critical thinking skills through careful analysis, reasoned inference, and thoughtful evaluation of contemporary culture and ideas. An engaging visual design developed with extensive student feedback and 15-page chapters makesTHINK Critically the textbook your students will actually read. It delivers the core concepts of critical thinking in a way they can easily understand. Additionally, engaging examples and masterful exercises help students learn to clarify ideas, analyze arguments, (...)
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  27.  44
    A Historical Introduction to the Philosophy of Mind: Readings with Commentary.Peter A. Morton - 1996 - Peterborough, CA: Broadview Press. Edited by Peter Morton.
    A Historical Introduction to the Philosophy of Mind is designed both to provide a selection of core readings on the subject and to make those readings accessible by providing commentaries to guide the reader through initially intimidating material. Each commentary explains technical concepts and provides background on obscure arguments as they arise, setting them in the historical and intellectual milieu from which they emerged. The readings concentrate on providing the student with a solid grounding in the theories of representative figures (...)
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  28.  8
    A Thomistic Tapestry: Essays in Memory of Étienne Gilson.Peter A. Redpath (ed.) - 2003 - BRILL.
    This book, written by well-known students of Étienne Gilson and especially dedicated to Armand A. Maurer, helps inaugurate a long-overdue special series in philosophy honoring Gilson’s legendary scholarship. It presents wide-ranging expositions of Thomist realism in the tradition of Gilsonian humanism covering themes related to philosophy in general, historical method, aesthetics, metaphysics, epistemology, and politics.
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  29.  45
    Philosophy of Mind: Historical and Contemporary Perspectives - Third Edition.Peter A. Morton & Myrto Mylopoulos (eds.) - 2020 - Peterborough, CA: Broadview Press.
    This book introduces students to the principal issues in the philosophy of mind by tracing the history of the subject from Plato and Aristotle through to the present day. Over forty primary-source readings are included. Extensive commentaries from the editors are provided to guide student readers through the arguments and jargon and to offer necessary historical context for the readings. The new third edition examines some of the most exciting recent developments in the field, including advances in theories about the (...)
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  30.  7
    The Great Ideas of Religion and Freedom: A Semiotic Reinterpretation of The Great Ideas Movement for the 21st Century.Peter A. Redpath, Imelda Chłodna-Błach & Artur Mamcarz-Plisiecki (eds.) - 2021 - BRILL.
    This collective volume offers the radically new thesis that, generically-considered, philosophy and science are identical and great because they are mainly psychological forms of wondering about organizational formation and operation, forms of behavioral organizational and leadership psychology.
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  31.  21
    Cartesian Nightmare: An Introduction to Transcendental Sophistry.Peter A. Redpath (ed.) - 1997 - Brill | Rodopi.
    This book challenges the presupposition among professional philosophers that René Descartes is the Father of Modern Philosophy. It demonstrates by intensive textual analysis of Descartes's _Discourse_ and _Meditations_ that he inaugurated a new type of sophistry rather than a new way of conducting philosophy. Transcendental Sophistry is a synthesis of Renaissance humanism and Christian theology, especially the theology of creation. This striking re-evaluation of the achievement of Descartes opens the history of Western philosophy to radical reinterpretation.
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  32. Jacques Maritain.Peter A. Redpath - 2009 - In Graham Oppy & Nick Trakakis (eds.), Medieval Philosophy of Religion: The History of Western Philosophy of Religion, Volume 2. Routledge. pp. 5--105.
     
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  33.  59
    Strengthening Morality and Ethics in Educational Assessment through Ubuntu in South Africa.Peter A. D. Beets - 2012 - Educational Philosophy and Theory 44 (s2):68-83.
    While assessment is regarded as integral to enhancing the quality of teaching and learning, it is also a practice fraught with moral and ethical issues. An analysis is made of current assessment practices of teachers in South Africa which seem to straddle the domains of accountability and professional codes of conduct. In the process the position of the teacher as mediator between policies and diverse learner needs is explored in the light of moral and ethical considerations. Based on the notions (...)
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  34. The Corporation as a Moral Person.Peter A. French - 1979 - American Philosophical Quarterly 16 (3):207 - 215.
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  35. The re-emergence of emergence, and the causal role of synergy in emergent evolution.Peter A. Corning - 2012 - Synthese 185 (2):295-317.
    Despite its current popularity, “emergence” is a concept with a venerable history and an elusive, ambiguous standing in contemporary evolutionary theory. This paper briefly recounts the history of the term and details some of its current usages. Not only are there radically varying interpretations about how to define emergence but “reductionist” and “holistic” theorists hold very different views about the issue of causation. However, these two seemingly polar positions are not irreconcilable. Reductionism, or detailed analysis of the parts and their (...)
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  36.  33
    Placebo Surgery for Parkinson's Disease: Do the Benefits Outweigh the Risks?Peter A. Clark - 2002 - Journal of Law, Medicine and Ethics 30 (1):58-68.
    In April 1999, Dr. Curt Freed of the University of Colorado in Denver and Dr. Stanley Fahn of Columbia Presbyterian Center in New York presented the results of a four-year, $5.7 million government-financed study using tissue from aborted fetuses to treat Parkinson’s disease at a conference of the American Academy of Neurology. The results of the first government-financed, placebo-controlled clinical study using fetal tissue showed that the symptoms of some Parkinson’s patients had been relieved. This research study involved forty subjects, (...)
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  37.  85
    The semasiology of some primary confucian concepts.Peter A. Boodberg - 1953 - Philosophy East and West 2 (4):317-332.
  38.  43
    Mother-to-child transmission of hiv in botswana: An ethical perspective on mandatory testing.Peter A. Clark - 2006 - Developing World Bioethics 6 (1):1–12.
    ABSTRACTMother‐to‐child transmission of HIV represents a particularly dramatic aspect of the HIV epidemic with an estimated 600,000 newborns infected yearly, 90% of them living in sub‐Saharan Africa. Since the beginning of the HIV epidemic, an estimated 5.1 million children worldwide have been infected with HIV. MTCT is responsible for 90% of these infections. Two‐thirds of the MTCT are believed to occur during pregnancy and delivery, and about one‐third through breastfeeding. As the number of women of child bearing age infected with (...)
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  39.  62
    The Cambridge textbook of bioethics.Peter A. Singer & A. M. Viens (eds.) - 2008 - New York: Cambridge University Press.
    Medicine and health care generate many bioethical problems and dilemmas that are of great academic, professional and public interest. This comprehensive resource is designed as a succinct yet authoritative text and reference for clinicians, bioethicists, and advanced students seeking a better understanding of ethics problems in the clinical setting. Each chapter illustrates an ethical problem that might be encountered in everyday practice; defines the concepts at issue; examines their implications from the perspectives of ethics, law and policy; and then provides (...)
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  40.  19
    Mind, Psychoanalysis, and Science.Peter A. Clark & Crispin Wright (eds.) - 1988 - Blackwell.
  41. A Sketch of a Theory of Moral Blameworthiness.Peter A. Graham - 2014 - Philosophy and Phenomenological Research 88 (2):388-409.
    In this paper I sketch an account of moral blame and blameworthiness. I begin by clarifying what I take blame to be and explaining how blameworthiness is to be analyzed in terms of it. I then consider different accounts of the conditions of blameworthiness and, in the end, settle on one according to which a person is blameworthy for φ-ing just in case, in φ-ing, she violates one of a particular class of moral requirements governing the attitudes we bear, and (...)
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  42.  68
    The sense of ugliness.Peter A. Carmichael - 1972 - Journal of Aesthetics and Art Criticism 30 (4):495-498.
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  43. Deontological decision theory and lesser-evil options.Seth Lazar & Peter A. Graham - 2021 - Synthese (7):1-28.
    Normative ethical theories owe us an account of how to evaluate decisions under risk and uncertainty. Deontologists seem at a disadvantage here: our best decision theories seem tailor-made for consequentialism. For example, decision theory enjoins us to always perform our best option; deontology is more permissive. In this paper, we discuss and defend the idea that, when some pro-tanto wrongful act is all-things considered permissible, because it is a ‘lesser evil’, it is often merely permissible, by the lights of deontology. (...)
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  44.  37
    Physician Participation in Executions: Care Giver or Executioner?Peter A. Clark - 2006 - Journal of Law, Medicine and Ethics 34 (1):95-104.
    To circumvent objections that the death penalty was “cruel and unusual punishment” and therefore a violation of the Eighth Amendment to the Constitution, advocates proposed lethal injection and the involvement of physicians to overcome the negative perceptions associated with the death penalty, and to increase public acceptability of the practice. Initiated in 1982, lethal injection is now the primary method of execution in 37 of the 38 states with the death penalty. “To be exact, this method has been used to (...)
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  45.  9
    The God Particle: If the Universe Is the Answer, What Is the Question?. Leon Lederman, Dick TeresiDreams of a Final Theory. Steven Weinberg.Peter A. Degen - 1994 - Isis 85 (4):736-738.
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  46.  67
    Does Elusive Becoming in Fact Characterize H. D. Lewis' View of the Mind?: PETER A. BERTOCCI.Peter A. Bertocci - 1979 - Religious Studies 15 (3):399-405.
    It was a little over ten years ago, 1967–8, that H. D. Lewis delivered the first series of Gifford lectures, The Elusive Mind, in the University of Edinburgh. It was my privilege that year to be an auditor in the Seminar at King's College that Professor Lewis was conducting with his students in the area of this topic. I had already read the works in which, in the midst of neo-orthodox and existentialist religious movements, he had devoted himself to critical (...)
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  47.  67
    The re‐emergence of “emergence”: A venerable concept in search of a theory.Peter A. Corning - 2002 - Complexity 7 (6):18-30.
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  48.  7
    Mother‐to‐Child Transmission of Hiv in Botswana: An Ethical Perspective on Mandatory Testing.Peter A. Clark - 2006 - Developing World Bioethics 6 (1):1-12.
    ABSTRACT Mother‐to‐child transmission (MTCT) of HIV represents a particularly dramatic aspect of the HIV epidemic with an estimated 600,000 newborns infected yearly, 90% of them living in sub‐Saharan Africa. Since the beginning of the HIV epidemic, an estimated 5.1 million children worldwide have been infected with HIV. MTCT is responsible for 90% of these infections. Two‐thirds of the MTCT are believed to occur during pregnancy and delivery, and about one‐third through breastfeeding. As the number of women of child bearing age (...)
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  49. In defense of objectivism about moral obligation.Peter A. Graham - 2010 - Ethics 121 (1):88-115.
    There is a debate in normative ethics about whether or not our moral obligations depend solely on either our evidence concerning, or our beliefs about, the world. Subjectivists maintain that they do and objectivists maintain that they do not. I shall offer some arguments in support of objectivism and respond to the strongest argument for subjectivism. I shall also briefly consider the significance of my discussion to the debate over whether one’s future voluntary actions are relevant to one’s current moral (...)
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  50.  17
    Toward a Metaphysics of Creation.Peter A. Bertocci - 1964 - Review of Metaphysics 17 (4):493 - 510.
    Creative change characterizes the nature of god, And a temporalistic form of personalistic theism can illuminate human experience. To establish this thesis, The author first discusses the logical, Metaphysical, And religious bases for the traditional view that ultimate being must be perfect and unchanging. He then proposes an alternate model of reason, Presents a concept of persons as active unities capable of maintaining their self-Identity through change, And argues for the possibility of creation ex nihilo. Finally, After discussing valid classical (...)
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