Results for 'Reed Solomon'

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  1.  34
    Reverse mathematics and the equivalence of definitions for well and better quasi-orders.Peter Cholak, Alberto Marcone & Reed Solomon - 2004 - Journal of Symbolic Logic 69 (3):683-712.
  2.  18
    Separating principles below Ramsey's theorem for pairs.Manuel Lerman, Reed Solomon & Henry Towsner - 2013 - Journal of Mathematical Logic 13 (2):1350007.
    In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.
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  3. Reverse Mathematics and Fully Ordered Groups.Reed Solomon - 1998 - Notre Dame Journal of Formal Logic 39 (2):157-189.
    We study theorems of ordered groups from the perspective of reverse mathematics. We show that suffices to prove Hölder's Theorem and give equivalences of both (the orderability of torsion free nilpotent groups and direct products, the classical semigroup conditions for orderability) and (the existence of induced partial orders in quotient groups, the existence of the center, and the existence of the strong divisible closure).
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  4.  26
    Π10 classes and orderable groups.Reed Solomon - 2002 - Annals of Pure and Applied Logic 115 (1-3):279-302.
    It is known that the spaces of orders on orderable computable fields can represent all Π10 classes up to Turing degree. We show that the spaces of orders on orderable computable abelian and nilpotent groups cannot represent Π10 classes in even a weak manner. Next, we consider presentations of ordered abelian groups, and we show that there is a computable ordered abelian group for which no computable presentation admits a computable set of representatives for its Archimedean classes.
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  5. On the filter of computably enumerable supersets of an r-maximal set.Steffen Lempp, André Nies & D. Reed Solomon - 2001 - Archive for Mathematical Logic 40 (6):415-423.
    We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0 3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).
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  6. Ordered groups: A case study in reverse mathematics.Reed Solomon - 1999 - Bulletin of Symbolic Logic 5 (1):45-58.
    The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of mathematics. In addition to being interesting in their own right, answers to this question have consequences in both effective mathematics and the foundations of mathematics. Before discussing these consequences, we need to be more specific about the motivating question.Reverse mathematics is useful for studying theorems of either countable or essentially countable mathematics. Essentially countable mathematics is a vague term that is (...)
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  7. – CA 0 and order types of countable ordered groups.Reed Solomon - 2001 - Journal of Symbolic Logic 66 (1):192-206.
  8. Effectiveness for infinite variable words and the Dual Ramsey Theorem.Joseph S. Miller & Reed Solomon - 2004 - Archive for Mathematical Logic 43 (4):543-555.
    We examine the Dual Ramsey Theorem and two related combinatorial principles VW(k,l) and OVW(k,l) from the perspectives of reverse mathematics and effective mathematics. We give a statement of the Dual Ramsey Theorem for open colorings in second order arithmetic and formalize work of Carlson and Simpson [1] to show that this statement implies ACA 0 over RCA 0 . We show that neither VW(2,2) nor OVW(2,2) is provable in WKL 0 . These results give partial answers to questions posed by (...)
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  9.  27
    Reverse mathematics and infinite traceable graphs.Peter Cholak, David Galvin & Reed Solomon - 2012 - Mathematical Logic Quarterly 58 (1-2):18-28.
    We analyze three applications of Ramsey’s Theorem for 4-tuples to infinite traceable graphs and finitely generated infinite lattices using the tools of reverse mathematics. The applications in graph theory are shown to be equivalent to Ramsey’s Theorem while the application in lattice theory is shown to be provable in the weaker system RCA0.
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  10.  31
    The complexity of central series in nilpotent computable groups.Barbara F. Csima & Reed Solomon - 2011 - Annals of Pure and Applied Logic 162 (8):667-678.
    The terms of the upper and lower central series of a nilpotent computable group have computably enumerable Turing degree. We show that the Turing degrees of these terms are independent even when restricted to groups which admit computable orders.
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  11.  19
    2010 North American Annual Meeting of the Association for Symbolic Logic.Reed Solomon - 2011 - Bulletin of Symbolic Logic 17 (1):127-154.
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  12.  12
    Model completeness and relative decidability.Jennifer Chubb, Russell Miller & Reed Solomon - 2021 - Archive for Mathematical Logic 60 (6):721-735.
    We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} of a computably enumerable, model complete theory, the entire elementary diagram E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} must be decidable. We prove that indeed a c.e. theory T is model complete if and only if there is a (...)
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  13.  8
    Lowness for isomorphism, countable ideals, and computable traceability.Johanna N. Y. Franklin & Reed Solomon - 2020 - Mathematical Logic Quarterly 66 (1):104-114.
    We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune free degrees, lowness for isomorphism is entirely independent of computable traceability.
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  14.  29
    The uniform content of partial and linear orders.Eric P. Astor, Damir D. Dzhafarov, Reed Solomon & Jacob Suggs - 2017 - Annals of Pure and Applied Logic 168 (6):1153-1171.
  15.  13
    The determined property of baire in reverse math.Eric P. Astor, Damir Dzhafarov, Antonio Montalbán, Reed Solomon & Linda Brown Westrick - 2020 - Journal of Symbolic Logic 85 (1):166-198.
    We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle $CD - PB$, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than $AT{R_0}$. Any ω-model of $CD - PB$ must be closed under hyperarithmetic reduction, but $CD - PB$ is not a theory of hyperarithmetic analysis. We show that whenever $M \subseteq {2^\omega }$ is the second-order part of an ω-model (...)
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  16.  63
    Jump degrees of torsion-free abelian groups.Brooke M. Andersen, Asher M. Kach, Alexander G. Melnikov & Reed Solomon - 2012 - Journal of Symbolic Logic 77 (4):1067-1100.
    We show, for each computable ordinal α and degree $\alpha > {0^{\left( \alpha \right)}}$, the existence of a torsion-free abelian group with proper α th jump degree α.
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  17. and the existence of strong divisible closures (ACA0). Section 8 deals more directly with computability issues and discusses the relationship between Π0. [REVIEW]Reed Solomon - 1999 - Bulletin of Symbolic Logic 5 (1).
  18.  68
    Enumerations in computable structure theory.Sergey Goncharov, Valentina Harizanov, Julia Knight, Charles McCoy, Russell Miller & Reed Solomon - 2005 - Annals of Pure and Applied Logic 136 (3):219-246.
    We exploit properties of certain directed graphs, obtained from the families of sets with special effective enumeration properties, to generalize several results in computable model theory to higher levels of the hyperarithmetical hierarchy. Families of sets with such enumeration features were previously built by Selivanov, Goncharov, and Wehner. For a computable successor ordinal α, we transform a countable directed graph into a structure such that has a isomorphic copy if and only if has a computable isomorphic copy.A computable structure is (...)
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  19.  83
    A Δ20 set with no infinite low subset in either it or its complement.Rod Downey, Denis R. Hirschfeldt, Steffen Lempp & Reed Solomon - 2001 - Journal of Symbolic Logic 66 (3):1371-1381.
    We construct the set of the title, answering a question of Cholak, Jockusch, and Slaman [1], and discuss its connections with the study of the proof-theoretic strength and effective content of versions of Ramsey's Theorem. In particular, our result implies that every ω-model of RCA 0 + SRT 2 2 must contain a nonlow set.
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  20. 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.
  21.  36
    Self-Embeddings of Computable Trees.Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman, James H. Schmerl & Reed Solomon - 2008 - Notre Dame Journal of Formal Logic 49 (1):1-37.
    We divide the class of infinite computable trees into three types. For the first and second types, 0' computes a nontrivial self-embedding while for the third type 0'' computes a nontrivial self-embedding. These results are optimal and we obtain partial results concerning the complexity of nontrivial self-embeddings of infinite computable trees considered up to isomorphism. We show that every infinite computable tree must have either an infinite computable chain or an infinite Π01 antichain. This result is optimal and has connections (...)
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  22. Degrees of orders on torsion-free Abelian groups.Asher M. Kach, Karen Lange & Reed Solomon - 2013 - Annals of Pure and Applied Logic 164 (7-8):822-836.
    We show that if H is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy G of H such that G has computable orders but not orders of every degree.
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  23. Stability and Posets.Carl G. Jockusch, Bart Kastermans, Steffen Lempp, Manuel Lerman & Reed Solomon - 2009 - Journal of Symbolic Logic 74 (2):693-711.
    Hirschfeldt and Shore have introduced a notion of stability for infinite posets. We define an arguably more natural notion called weak stability, and we study the existence of infinite computable or low chains or antichains, and of infinite $\Pi _1^0 $ chains and antichains, in infinite computable stable and weakly stable posets. For example, we extend a result of Hirschfeldt and Shore to show that every infinite computable weakly stable poset contains either an infinite low chain or an infinite computable (...)
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  24.  40
    The lindenbaum algebra of the theory of the class of all finite models.Steffen Lempp, Mikhail Peretyat'kin & Reed Solomon - 2002 - Journal of Mathematical Logic 2 (02):145-225.
    In this paper, we investigate the Lindenbaum algebra ℒ of the theory T fin = Th of the class M fin of all finite models of a finite rich signature. We prove that this algebra is an atomic Boolean algebra while its Gödel numeration γ is a [Formula: see text]-numeration. Moreover, the quotient algebra /ℱ, γ/ℱ) modulo the Fréchet ideal ℱ is a [Formula: see text]-algebra, which is universal over the class of all [Formula: see text] Boolean algebras. These conditions (...)
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  25.  13
    On the isomorphism problem for some classes of computable algebraic structures.Valentina S. Harizanov, Steffen Lempp, Charles F. D. McCoy, Andrei S. Morozov & Reed Solomon - 2022 - Archive for Mathematical Logic 61 (5):813-825.
    We establish that the isomorphism problem for the classes of computable nilpotent rings, distributive lattices, nilpotent groups, and nilpotent semigroups is \-complete, which is as complicated as possible. The method we use is based on uniform effective interpretations of computable binary relations into computable structures from the corresponding algebraic classes.
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  26.  26
    Embeddings of Computable Structures.Asher M. Kach, Oscar Levin & Reed Solomon - 2010 - Notre Dame Journal of Formal Logic 51 (1):55-68.
    We study what the existence of a classical embedding between computable structures implies about the existence of computable embeddings. In particular, we consider the effect of fixing and varying the computable presentations of the computable structures.
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  27. On a Conjecture of Dobrinen and Simpson concerning Almost Everywhere Domination.Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman & Reed Solomon - 2006 - Journal of Symbolic Logic 71 (1):119 - 136.
  28.  54
    New Orleans Marriott and Sheraton New Orleans New Orleans, Louisiana January 7–8, 2007.Matthew Foreman, Su Gao, Valentina Harizanov, Ulrich Kohlenbach, Michael Rathjen, Reed Solomon, Carol Wood & Marcia Groszek - 2007 - Bulletin of Symbolic Logic 13 (3).
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  29.  54
    Computable categoricity of trees of finite height.Steffen Lempp, Charles McCoy, Russell Miller & Reed Solomon - 2005 - Journal of Symbolic Logic 70 (1):151-215.
    We characterize the structure of computably categorical trees of finite height, and prove that our criterion is both necessary and sufficient. Intuitively, the characterization is easiest to express in terms of isomorphisms of (possibly infinite) trees, but in fact it is equivalent to a Σ03-condition. We show that all trees which are not computably categorical have computable dimension ω. Finally, we prove that for every n≥ 1 in ω, there exists a computable tree of finite height which is δ0n+1-categorical but (...)
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  30. List Decoding of Reed-Solomon Codes.E. van Niekerk - 1997 - Complexity 13:180-193.
     
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  31.  95
    S. S. Goncharov. Autostability and computable families of constructivizations. Algebra and Logic, vol. 14 , no. 6, pp. 392–409. - S. S. Goncharov. The quantity of nonautoequivalent constructivizations. Algebra and Logic, vol. 16 , no. 3, pp. 169–185. - S. S. Goncharov and V. D. Dzgoev. Autostability of models. Algebra and Logic, vol. 19 , no. 1, pp. 28–37. - J. B. Remmel. Recursively categorical linear orderings. Proceedings of the American Mathematical Society, vol. 83 , no. 2, pp. 387–391. - Terrence Millar. Recursive categoricity and persistence. The Journal of Symbolic Logic, vol. 51 , no. 2, pp. 430–434. - Peter Cholak, Segey Goncharov, Bakhadyr Khoussainov and Richard A. Shore. Computably categorical structures and expansions by constants. The Journal of Symbolic Logic, vol. 64 , no. 1, pp. 13–137. - Peter Cholak, Richard A. Shore and Reed Solomon. A computably stable structure with no Scott family of finitary formulas. Archive for Mathematical Logic, vol. 45 , no. 5, pp. 519–538. [REVIEW]Daniel Turetsky - 2012 - Bulletin of Symbolic Logic 18 (1):131-134.
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  32.  6
    S. S. Goncharov. Autostability and computable families of constructivizations. Algebra and Logic, vol. 14 (1975), no. 6, pp. 392–409. - S. S. Goncharov. The quantity of nonautoequivalent constructivizations. Algebra and Logic, vol. 16 (1977), no. 3, pp. 169–185. - S. S. Goncharov and V. D. Dzgoev. Autostability of models. Algebra and Logic, vol. 19 (1980), no. 1, pp. 28–37. - J. B. Remmel. Recursively categorical linear orderings. Proceedings of the American Mathematical Society, vol. 83 (1981), no. 2, pp. 387–391. - Terrence Millar. Recursive categoricity and persistence. The Journal of Symbolic Logic, vol. 51 (1986), no. 2, pp. 430–434. - Peter Cholak, Segey Goncharov, Bakhadyr Khoussainov and Richard A. Shore. Computably categorical structures and expansions by constants. The Journal of Symbolic Logic, vol. 64 (1999), no. 1, pp. 13–137. - Peter Cholak, Richard A. Shore and Reed Solomon. A computably stable structure with no Scott family of finitary formulas. Archive for Mathematical. [REVIEW]Daniel Turetsky - 2012 - Bulletin of Symbolic Logic 18 (1):131-134.
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  33. Victims of Circumstances? A Defense of Virtue Ethics in Business.Robert C. Solomon - 2003 - Business Ethics Quarterly 13 (1):43-62.
    Abstract:Should the responsibilities of business managers be understood independently of the social circumstances and “market forces” that surround them, or (in accord with empiricism and the social sciences) are agents and their choices shaped by their circumstances, free only insofar as they act in accordance with antecedently established dispositions, their “character”? Virtue ethics, of which I consider myself a proponent, shares with empiricism this emphasis on character as well as an affinity with the social sciences. But recent criticisms of both (...)
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  34. Ethics and excellence: cooperation and integrity in business.Robert C. Solomon - 1992 - New York: Oxford University Press.
    The Greek philosopher Aristotle, writing over two thousand years before Wall Street, called people who engaged in activities which did not contribute to society "parasites." In his latest work, renowned scholar Robert C. Solomon asserts that though capitalism may require capital, but it does not require, much less should it be defined by the parasites it inevitably attracts. Capitalism has succeeded not with brute strength or because it has made people rich, but because it has produced responsible citizens and--however (...)
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  35. A better way to think about business: how personal integrity leads to corporate success.Robert C. Solomon - 1999 - New York: Oxford University Press.
    Is business ethics a contradiction in terms? Absolutely not, says Robert Solomon. In fact, he maintains that sound ethics is a necessary precondition of any long-term business enterprise, and that excellence in business must exist on the foundation of values that most of us hold dear. Drawing on twenty years of experience consulting with major corporations on ethics, Solomon clarifies the difficult ethical choices all people in business are faced with from time to time. He takes an "Aristotelian" (...)
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  36.  20
    About love: reinventing romance for our times.Robert C. Solomon - 1994 - Indianapolis: Hackett Pub. Co..
    A subtle and distinguished work by a philosopher renowned for his groundbreaking analysis of human emotions, About Love.
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  37.  64
    The joy of philosophy: thinking thin versus the passionate life.Robert C. Solomon - 1999 - New York: Oxford University Press.
    The Joy of Philosophy is a return to some of the perennial questions of philosophy--questions about the meaning of life; about death and tragedy; about the respective roles of rationality and passion in the good life; about love, compassion, and revenge; about honesty, deception, and betrayal; and about who we are and how we think about who we are. Recapturing the heart-felt confusion and excitement that originally brings us all to philosophy, internationally renowned teacher and lecturer Robert C. Solomon (...)
  38.  8
    Tales of woe.John Reed - 2010 - Brooklyn, NY: PowerHouse Books.
    "In the 25 essays that comprise this grimly fascinating volume, Reed shines a light into some very dark corners. From its opening tale of South African baboons with a taste for human babies to a thoroughly icky account of a middle-aged woman's seduction of young boys, these are literary snapshots of the world at its worst."--Amazon.com.
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  39. Tarski's conceptual analysis of semantical notions.Solomon Feferman - 2008 - In Douglas Patterson (ed.), New essays on Tarski and philosophy. Oxford University Press. pp. 72.
  40. Global climate projections.S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor & H. L. Miller - 2007 - In S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor & H. L. Miller (eds.), Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press.
  41.  97
    Kant's Criticisms of Hume's Dialogues Concerning Natural Religion.Reed Winegar - 2015 - British Journal for the History of Philosophy 23 (5):888-910.
    According to recent commentators like Paul Guyer, Kant agrees with Hume's Dialogues Concerning Natural Religion that physico-theology can never provide knowledge of God and that the concept of God, nevertheless, provides a useful heuristic principle for scientific enquiry. This paper argues that Kant, far from agreeing with Hume, criticizes Hume's Dialogues for failing to prove that physico-theology can never yield knowledge of God and that Kant correctly views Hume's Dialogues as a threat to, rather than an anticipation of, his own (...)
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  42.  26
    In the spirit of Hegel: a study of G.W.F. Hegel's Phenomenology of spirit.Robert C. Solomon - 1983 - New York: Oxford University Press.
    The Phenomenology of Spirit was Hegel's grandest experiement, changing our vision of the world and the very nature of philosophical enterprise. In this book, Solomon captures the bold and exhilarating spirit, presenting the Phenomenology as a thoroughly personal as well as philosophical work. He begins with a historical introduction, which lays the groundwork for a section-by-section analysis of the Phenomenology. Both the initiated as well as readers unacquainted with the intricacies of German idealism will find this to be an (...)
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  43.  86
    Morality and the good life: an introduction to ethics through classical sources.Robert C. Solomon - 2009 - Boston: McGraw-Hill Higher Education. Edited by Clancy W. Martin & Wayne Vaught.
    Introduction -- What is ethics? -- Ethics and religion -- The history of ethics -- Ethical questions -- What is the good life? -- Why be good : the problem of justification -- Why be rational : the place of reason in ethics -- Which is right : ethical dilemmas -- Ethical concepts -- Universality -- Prudence and morals -- Happiness and the good -- Egoism and altruism -- Virtue and the virtues -- Facts and values -- Justice and equality (...)
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  44.  61
    A short history of philosophy.Robert C. Solomon - 1996 - New York: Oxford University Press. Edited by Kathleen Marie Higgins.
    In this accessible and comprehensive work, Robert Solomon and Kathleen Higgins cover the entire history of philosophy--ancient, medieval, and modern, from cultures both East and West--in its broader historical and cultural contexts. Major philosophers and movements are discussed along with less well-known but interesting figures. The authors examine the early Greek, Indic, and Chinese philosophers and the mythological traditions that preceded them, as well as the great religious philosophies, including Christianity, Hinduism, Judaism, and Taoism. Easily understandable to students without (...)
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  45.  6
    Business Ethics and Virtue.Robert C. Solomon - 1999 - In Robert Frederick (ed.), A companion to business ethics. Malden, Mass.: Blackwell. pp. 30–37.
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  46. Global Health and Global Health Ethics.Solomon Benatar & Gillian Brock (eds.) - 2011 - Cambridge University Press.
    Machine generated contents note: Preface; Introduction; Part I. Global Health, Definitions and Descriptions: 1. What is global health? Solly Benatar and Ross Upshur; 2. The state of global health in a radically unequal world: patterns and prospects Ron Labonte and Ted Schrecker; 3. Addressing the societal determinants of health: the key global health ethics imperative of our times Anne-Emmanuelle Birn; 4. Gender and global health: inequality and differences Lesley Doyal and Sarah Payne; 5. Heath systems and health Martin McKee; Part (...)
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  47. Socrates, Philosophy, and Friendship in the 'Phaedo'.Doug Reed - 2020 - In Wisdom, Love, and Friendship in Ancient Greek Philosophy: Essays in Honor of Daniel Devereux. Berlin, Germany: De Gruyter. pp. 175–190.
    In this paper I investigate Socrates as a friend in Plato's 'Phaedo'. I begin by setting out his friends' request for reassurance of how they will fare after Socrates dies. I argue that by structuring the discussion as he does, Socrates provides one final opportunity for his friends to prepare themselves for life without him, thus offering them the best kind of reassurance they could ask for.
     
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  48.  18
    Approximating Future Generic Entry for New Drugs.Reed F. Beall, Jonathan J. Darrow & Aaron S. Kesselheim - 2019 - Journal of Law, Medicine and Ethics 47 (1):177-182.
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  49. Thinking About Feeling: Contemporary Philosophers on Emotions.Robert C. Solomon (ed.) - 2004 - New York: Oxford University Press USA.
    Philosophers since Aristotle have explored emotion, and the study of emotion has always been essential to the love of wisdom. In recent years Anglo-American philosophers have rediscovered and placed new emphasis on this very old discipline. The view that emotions are ripe for philosophical analysis has been supported by a considerable number of excellent publications. In this volume, Robert Solomon brings together some of the best Anglo-American philosophers now writing on the philosophy of emotion, with chapters from philosophers who (...)
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  50. In defense of sentimentality.Robert C. Solomon - 2004 - New York: Oxford University Press.
    Philosophy has as much to do with feelings as it does with thoughts and thinking. Philosophy, accordingly, requires not only emotional sensitivity but an understanding of the emotions, not as curious but marginal psychological phenomena but as the very substance of life. In this, the second book in a series devoted to his work on the emotions, Robert Solomon presents a defense of the emotions and of sentimentality against the background of what he perceives as a long history of (...)
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