Results for ' Kurtz randomness'

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  1. Higher kurtz randomness.Bjørn Kjos-Hanssen, André Nies, Frank Stephan & Liang Yu - 2010 - Annals of Pure and Applied Logic 161 (10):1280-1290.
    A real x is -Kurtz random if it is in no closed null set . We show that there is a cone of -Kurtz random hyperdegrees. We characterize lowness for -Kurtz randomness as being -dominated and -semi-traceable.
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  2.  39
    Lowness for Kurtz randomness.Noam Greenberg & Joseph S. Miller - 2009 - Journal of Symbolic Logic 74 (2):665-678.
    We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, (...)
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  3.  18
    Moral Choices in a Random Universe.Paul Kurtz - 2013 - Essays in the Philosophy of Humanism 21 (2):103-110.
    This essay is excerpted by Nathan Bupp from Paul Kurtz, The Turbulent Universe (Amherst, N.Y.: Prometheus Books, 2013). Copyright ©2013 by the Estate of Paul Kurtz. All rights reserved. Used by permission of the Estate and the publisher, www.prometheusbooks.com.
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  4.  21
    André Nies. Lowness properties and randomness. Advances in Mathematics, vol. 197 , no. 1, pp. 274–305. - Bjørn Kjos-Hanssen, André Nies, and Frank Stephan. Lowness for the class of Schnorr random reals. SIAM Journal on Computing, vol. 35 , no. 3, pp. 647–657. - Noam Greenberg and Joseph S. Miller. Lowness for Kurtz randomness. The Journal of Symbolic Logic, vol. 74 , no. 2, pp. 665–678. - Laurent Bienvenu and Joseph S. Miller. Randomness and lowness notions via open covers. Annals of Pure and Applied Logic, vol. 163 , no. 5, pp. 506–518. - Johanna N. Y. Franklin, Frank Stephan, and Liang. Yu Relativizations of randomness and genericity notions. The Bulletin of the London Mathematical Society, vol. 43 , no. 4, pp. 721–733. - George Barmpalias, Joseph S. Miller, and André Nies. Randomness notions and partial relativization. Israel Journal of Mathematics, vol. 191 , no. 2, pp. 791–816. [REVIEW]Johanna N. Y. Franklin - 2013 - Bulletin of Symbolic Logic 19 (1):115-118.
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  5.  60
    Reviewed Work(s): Lowness properties and randomness. Advances in Mathematics, vol. 197 by André Nies; Lowness for the class of Schnorr random reals. SIAM Journal on Computing, vol. 35 by Bjørn Kjos-Hanssen; André Nies; Frank Stephan; Lowness for Kurtz randomness. The Journal of Symbolic Logic, vol. 74 by Noam Greenberg; Joseph S. Miller; Randomness and lowness notions via open covers. Annals of Pure and Applied Logic, vol. 163 by Laurent Bienvenu; Joseph S. Miller; Relativizations of randomness and genericity notions. The Bulletin of the London Mathematical Society, vol. 43 by Johanna N. Y. Franklin; Frank Stephan; Liang Yu; Randomness notions and partial relativization. Israel Journal of Mathematics, vol. 191 by George Barmpalias; Joseph S. Miller; André Nies. [REVIEW]Johanna N. Y. Franklin - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.
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  6.  76
    Calibrating randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
    We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness (...)
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  7. Subclasses of the Weakly Random Reals.Johanna N. Y. Franklin - 2010 - Notre Dame Journal of Formal Logic 51 (4):417-426.
    The weakly random reals contain not only the Schnorr random reals as a subclass but also the weakly 1-generic reals and therefore the n -generic reals for every n . While the class of Schnorr random reals does not overlap with any of these classes of generic reals, their degrees may. In this paper, we describe the extent to which this is possible for the Turing, weak truth-table, and truth-table degrees and then extend our analysis to the Schnorr random and (...)
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  8.  27
    Uniform distribution and algorithmic randomness.Jeremy Avigad - 2013 - Journal of Symbolic Logic 78 (1):334-344.
    A seminal theorem due to Weyl [14] states that if $(a_n)$ is any sequence of distinct integers, then, for almost every $x \in \mathbb{R}$, the sequence $(a_n x)$ is uniformly distributed modulo one. In particular, for almost every $x$ in the unit interval, the sequence $(a_n x)$ is uniformly distributed modulo one for every computable sequence $(a_n)$ of distinct integers. Call such an $x$ UD random. Here it is shown that every Schnorr random real is UD random, but there are (...)
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  9.  7
    Luzin’s (n) and randomness reflection.Arno Pauly, Linda Westrick & Liang Yu - 2020 - Journal of Symbolic Logic:1-27.
    We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. (...)
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  10.  3
    Luzin’s (n) and randomness reflection.Arno Pauly, Linda Westrick & Liang Yu - 2022 - Journal of Symbolic Logic 87 (2):802-828.
    We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. (...)
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  11.  7
    Martin-Löf Randomness Implies Multiple Recurrence in Effectively Closed Sets.Rodney G. Downey, Satyadev Nandakumar & André Nies - 2019 - Notre Dame Journal of Formal Logic 60 (3):491-502.
    This work contributes to the program of studying effective versions of “almost-everywhere” theorems in analysis and ergodic theory via algorithmic randomness. Consider the setting of Cantor space {0,1}N with the uniform measure and the usual shift. We determine the level of randomness needed for a point so that multiple recurrence in the sense of Furstenberg into effectively closed sets P of positive measure holds for iterations starting at the point. This means that for each k∈N there is an (...)
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  12. Van Lambalgen's Theorem and High Degrees.Johanna N. Y. Franklin & Frank Stephan - 2011 - Notre Dame Journal of Formal Logic 52 (2):173-185.
    We show that van Lambalgen's Theorem fails with respect to recursive randomness and Schnorr randomness for some real in every high degree and provide a full characterization of the Turing degrees for which van Lambalgen's Theorem can fail with respect to Kurtz randomness. However, we also show that there is a recursively random real that is not Martin-Löf random for which van Lambalgen's Theorem holds with respect to recursive randomness.
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  13.  17
    Polynomial clone reducibility.Quinn Culver - 2014 - 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 (...)
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  14.  22
    Constructive equivalence relations on computable probability measures.Laurent Bienvenu & Wolfgang Merkle - 2009 - Annals of Pure and Applied Logic 160 (3):238-254.
    A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually defined with respect to the uniform measure on the set of all sequences, but extend canonically to other computable probability measures. This way each notion of randomness induces an equivalence relation on the computable probability measures where two measures are equivalent if they have the same set of random sequences. (...)
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  15.  5
    Partition Genericity and Pigeonhole Basis Theorems.Benoit Monin & Ludovic Patey - forthcoming - Journal of Symbolic Logic:1-29.
    There exist two main notions of typicality in computability theory, namely, Cohen genericity and randomness. In this article, we introduce a new notion of genericity, called partition genericity, which is at the intersection of these two notions of typicality, and show that many basis theorems apply to partition genericity. More precisely, we prove that every co-hyperimmune set and every Kurtz random is partition generic, and that every partition generic set admits weak infinite subsets, for various notions of weakness. (...)
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  16. Tolerance and revolution.Paul Kurtz & Svetozar Stojanović (eds.) - 1970 - Beograd,: Philosophical Society of Serbia.
     
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  17.  28
    The Moral Point of View: A Rational Basis of Ethics.Paul W. Kurtz - 1959 - Philosophy and Phenomenological Research 20 (2):277-278.
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  18.  7
    The Phenomenology of Moral Experience.Paul W. Kurtz - 1956 - Philosophy and Phenomenological Research 17 (1):127-128.
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  19.  4
    Faith and Moral Authority.Paul W. Kurtz - 1954 - Philosophy and Phenomenological Research 14 (3):424-424.
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  20.  10
    The Structure of Society.Paul W. Kurtz - 1953 - Philosophy and Phenomenological Research 14 (1):114-115.
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  21.  6
    System of Ethics.Paul W. Kurtz - 1958 - Philosophy and Phenomenological Research 19 (2):254-255.
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  22. Interpretationen zu den Logos-Fragmenten Heraklits.Ewald Kurtz - 1971 - New York,: G. Olms.
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  23.  2
    Language and human nature.Paul Kurtz (ed.) - 1971 - St. Louis, Mo.,: W.H. Green.
  24.  1
    The Judgment of History.Paul W. Kurtz - 1955 - Philosophy and Phenomenological Research 16 (2):281-281.
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  25. Persistence: Contemporary Readings.Sally Anne Haslanger & Roxanne Marie Kurtz (eds.) - 2006 - Bradford.
    How does an object persist through change? How can a book, for example, open in the morning and shut in the afternoon, persist through a change that involves the incompatible properties of being open and being shut? The goal of this reader is to inform and reframe the philosophical debate around persistence; it presents influential accounts of the problem that range from classic papers by W. V. O. Quine, David Lewis, and Judith Jarvis Thomson to recent work by contemporary philosophers. (...)
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  26.  1
    Philosophy: An Introduction.Paul W. Kurtz - 1954 - Philosophy and Phenomenological Research 15 (1):130-131.
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  27.  1
    Philosophical Problems of Psychology.Paul Kurtz - 1965 - Philosophy of Science 32 (2):202-203.
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  28.  10
    All the Mothers are One: Hindu India and the Cultural Reshaping of Psychoanalysis.Malcolm McLean & Stanley N. Kurtz - 1995 - Journal of the American Oriental Society 115 (4):690.
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  29. Moral problems in contemporary society.Paul Kurtz - 1969 - Englewood Cliffs, N.J.,: Prentice-Hall.
     
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  30. Quinean Ontological Commitment Derailed.Roxanne Marie Kurtz - 2013 - Analiza I Egzystencja 24:87-114.
     
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  31.  9
    Editors’ Introduction: Radical Philosophy and Politics Amid the Climate Crisis and the Coronavirus Pandemic.Harry van der Linden & Reed M. Kurtz - unknown
    Editors’ Introduction: Radical Philosophy and Politics Amid the Climate Crisis and the Coronavirus Pandemic for Radical Philosophy Review.
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  32.  1
    The Verbal Icon: Studies in the Meaning of Poetry.William Kurtz Wimsatt & Monroe C. Beardsley - 1970
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  33. Ethical Value.Paul W. Kurtz - 1957 - Philosophy and Phenomenological Research 18 (1):133-134.
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  34.  1
    Theory of Beauty.Paul W. Kurtz - 1954 - Philosophy and Phenomenological Research 14 (3):429-430.
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  35.  6
    The Philosophy of Value.Paul W. Kurtz - 1957 - Philosophy and Phenomenological Research 18 (2):284-285.
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  36.  4
    The court of wisdom convenes.Kurtz Paul - 2003 - Free Inquiry 23 (2):28.
    SPECIAL SECTION PHYSICIAN-ASSISTED SUICIDE, PRO AND CON.
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  37.  6
    The free market with a human face.Kurtz Paul - 2004 - Free Inquiry 24 (2):5.
  38.  5
    The war against iraq.Kurtz Paul - 2003 - Free Inquiry 23 (2):5.
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  39.  7
    Without religion.Kurtz Paul - 2002 - Free Inquiry 23 (1):5.
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  40.  48
    Frontiers of Knowledge in the Study of Man. [REVIEW]Paul W. Kurtz - 1958 - Journal of Philosophy 55 (10):435-438.
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  41.  4
    Paul Michael Kurtz: „Was wir von dem Siege erhoffen“. Eine Stellungnahme Hermann Gunkels zur Zeit des Ersten Weltkriegs.Paul Michael Kurtz - 2017 - Journal for the History of Modern Theology/Zeitschrift für Neuere Theologiegeschichte 24 (1):122-130.
    In an opinion piece penned at the Great War’s onset yet apparently unpublished until now, the historian of religion Hermann Gunkel outlined the opportunities he saw for the German people in anticipation of their triumph. He believed this war could consummate what the Napoleonic Wars and the Unification of Germany had not. Gunkel hoped for true German unity, more liberal domestic politics, and spiritual restoration. Further still, he referred to a resurgence of piety on account of the conflict. On the (...)
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  42.  22
    Beyond Standardization: Improving External Validity and Reproducibility in Experimental Evolution.Eric Desjardins, Joachim Kurtz, Nina Kranke, Ana Lindeza & S. Helene Richter - 2021 - BioScience 71 (5):543–552.
    Discussions of reproducibility are casting doubts on the credibility of experimental outcomes in the life sciences. Although experimental evolution is not typically included in these discussions, this field is also subject to low reproducibility, partly because of the inherent contingencies affecting the evolutionary process. A received view in experimental studies more generally is that standardization (i.e., rigorous homogenization of experimental conditions) is a solution to some issues of significance and internal validity. However, this solution hides several difficulties, including a reduction (...)
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  43.  3
    Toward A New Enlightenment: The Philosophy of Paul Kurtz.Paul Kurtz & Vern L. Bullough - 1994 - Routledge.
    Paul Kurtz has been the dominant voice of secular humanism over the past thirty years. This compilation of his work reveals the scope of his thinking on the basic topics of our time and his many and varied contributions to the cause of free thought. It focuses on the central issues that have concerned Kurtz throughout his career: ethics, politics, education, religion, science, and pseudoscience. The chapters are linked by a common theme: the need for a new enlightenment, (...)
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  44.  30
    Science and Values; Explorations in Philosophy and the Social Sciences. [REVIEW]Paul W. Kurtz - 1953 - Journal of Philosophy 50 (21):649-652.
  45.  36
    Relations, Objects, and the Composition of Analogies.Dedre Gentner & Kenneth J. Kurtz - 2006 - Cognitive Science 30 (4):609-642.
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  46.  38
    The Quest for Community; a Study in the Ethics of Order and Freedom. [REVIEW]Paul W. Kurtz - 1953 - Journal of Philosophy 50 (25):788-792.
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  47. John Wesley‘s editorial hand in Susanna Annesley Wesley‘s 1732 ‘Education’ letter.Elizabeth Kurtz Lynch - 2003 - Bulletin of the John Rylands Library 85 (2):195-208.
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  48.  23
    Recursion theory and ordered groups.R. G. Downey & Stuart A. Kurtz - 1986 - Annals of Pure and Applied Logic 32:137-151.
  49.  7
    Reliability of “the eye of the beholder”: Effects of sex of the beholder and sex of the beheld.Norbert L. Kerr & Susan Turner Kurtz - 1978 - Bulletin of the Psychonomic Society 12 (3):179-181.
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  50.  27
    Knowledge and Value: Introductory Readings in Philosophy. [REVIEW]Paul W. Kurtz - 1960 - Journal of Philosophy 57 (16):535-538.
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