Results for 'Urysohn Lemma'

514 found
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  1.  24
    A Constructive Treatment of Urysohn's Lemma in an Apartness Space.Douglas Bridges & Hannes Diener - 2006 - Mathematical Logic Quarterly 52 (5):464-469.
    This paper is dedicated to Prof. Dr. Günter Asser, whose work in founding this journal and maintaining it over many difficult years has been a major contribution to the activities of the mathematical logic community.At first sight it appears highly unlikely that Urysohn's Lemma has any significant constructive content. However, working in the context of an apartness space and using functions whose values are a generalisation of the reals, rather than real numbers, enables us to produce a significant (...)
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  2.  15
    Effective Borel Degrees of Some Topological Functions.Guido Gherardi - 2006 - Mathematical Logic Quarterly 52 (6):625-642.
    The focus of this paper is the incomputability of some topological functions using the tools of Borel computability theory, as introduced by V. Brattka in [3] and [4]. First, we analyze some basic topological functions on closed subsets of ℝn, like closure, border, intersection, and derivative, and we prove for such functions results of Σ02-completeness and Σ03-completeness in the effective Borel hierarchy. Then, following [13], we re-consider two well-known topological results: the lemmas of Urysohn and Urysohn-Tietze for generic (...)
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  3.  8
    Computable Metrization.Tanja Grubba, Matthias Schröder & Klaus Weihrauch - 2007 - Mathematical Logic Quarterly 53 (4‐5):381-395.
    Every second-countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space can be considered computationally as a subspace of some computable metric space [15]. While Schröder's construction is “pointless”, i. e., only sets of a countable base but no concrete points are known, for a computable metric space a concrete dense set of computable points (...)
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  4.  28
    Versions of Normality and Some Weak Forms of the Axiom of Choice.Paul Howard, Kyriakos Keremedis, Herman Rubin & Jean E. Rubin - 1998 - Mathematical Logic Quarterly 44 (3):367-382.
    We investigate the set theoretical strength of some properties of normality, including Urysohn's Lemma, Tietze-Urysohn Extension Theorem, normality of disjoint unions of normal spaces, and normality of Fσ subsets of normal spaces.
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  5.  4
    Reverse Mathematics of Topology: Dimension, Paracompactness, and Splittings.Sam Sanders - 2020 - Notre Dame Journal of Formal Logic 61 (4):537-559.
    Reverse mathematics is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, that is, non-set-theoretic, mathematics. As suggested by the title, this paper deals with the study of the topological notions of dimension and paracompactness, inside Kohlenbach’s higher-order RM. As to splittings, there are some examples in RM of theorems A, B, C such that A (...)
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  6.  1
    Off the Couch: Contemporary Psychoanalytic Applications.Alessandra Lemma & Matthew Patrick (eds.) - 2010 - Routledge.
    _Alessandra Lemma - Winner of the Levy-Goldfarb Award for Child Psychoanalysis!_ The contemporary relevance of psychoanalysis is being increasingly questioned; _Off the Couch_ challenges this view, demonstrating that psychoanalytic thinking and its applications are both innovative and relevant, in particular to the management and treatment of more disturbed and difficult to engage patient groups. Chapters address: clinical applications in diverse settings across the age range the relevance of psychoanalytic thinking to the practice of CBT, psychosomatics and general psychiatry the (...)
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  7.  4
    Pledger Lemma and the Modal System S3°.Bolesław Sobociński - 1976 - Notre Dame Journal of Formal Logic 17:253.
  8.  32
    Do Lemmas Speak German? A Verb Position Effect in German Structural Priming.Franklin Chang, Michael Baumann, Sandra Pappert & Hartmut Fitz - 2015 - Cognitive Science 39 (5):1113-1130.
    Lexicalized theories of syntax often assume that verb-structure regularities are mediated by lemmas, which abstract over variation in verb tense and aspect. German syntax seems to challenge this assumption, because verb position depends on tense and aspect. To examine how German speakers link these elements, a structural priming study was performed which varied syntactic structure, verb position, and verb overlap.structural priming was found, both within and across verb position, but priming was larger when the verb position was the same between (...)
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  9.  1
    A Lemma of Logarithmic Derivative for Some Δ-Subharmonic Functions.Atsushi Atsuji - 2001 - History and Philosophy of Logic 46 (3):195-206.
  10.  1
    More on Fréchet–Urysohn Ideals.Salvador García Ferreira & Osvaldo Guzmán - 2022 - Journal of Symbolic Logic 87 (2):829-851.
    We study the Rudin–Keisler pre-order on Fréchet–Urysohn ideals on $\omega $. We solve three open questions posed by S. García-Ferreira and J. E. Rivera-Gómez in the articles [5] and [6] by establishing the following results: •For every AD family $\mathcal {A},$ there is an AD family $\mathcal {B}$ such that $\mathcal {A}^{\perp } <_{{\textsf {RK}}}\mathcal {B}^{\perp }.$ •If $\mathcal {A}$ is a nowhere MAD family of size $\mathfrak {c}$ then there is a nowhere MAD family $\mathcal {B}$ such that (...)
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  11.  9
    Limit Lemmas and Jump Inversion in the Enumeration Degrees.Evan J. Griffiths - 2003 - Archive for Mathematical Logic 42 (6):553-562.
    We show that there is a limit lemma for enumeration reducibility to 0 e ', analogous to the Shoenfield Limit Lemma in the Turing degrees, which relativises for total enumeration degrees. Using this and `good approximations' we prove a jump inversion result: for any set W with a good approximation and any set X< e W such that W≤ e X' there is a set A such that X≤ e A< e W and A'=W'. (All jumps are enumeration (...)
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  12.  66
    An Irreflexivity Lemma with Applications to Axiomatizations of Conditions on Tense Frames.Dov M. Gabbay - 1981 - In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht. pp. 67--89.
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  13. The Diagonal Lemma: An Informal Exposition.Richard Kimberly Heck - manuscript
    This is a completely informal presentation of the ideas behind the diagonal lemma. One really can't see this important result from too many different angles. This one aims at getting the main idea across. (For the cognoscenti, it is in the spirit of Quine's treatment in terms of "appended to its own quotation".).
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  14.  12
    A Covering Lemma for $${K}$$.Daniel W. Cunningham - 2007 - Archive for Mathematical Logic 46 (3):197-221.
    The Dodd–Jensen Covering Lemma states that “if there is no inner model with a measurable cardinal, then for any uncountable set of ordinals X, there is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Y\in K}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq Y}$$\end{document} and |X| = |Y|”. Assuming ZF+AD alone, we establish the following analog: If there is no inner model with an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...)
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  15. To Be, or Not to Be? The Role of the Unconscious in Transgender Transitioning: Identity, Autonomy and Well-Being.Alessandra Lemma & Julian Savulescu - forthcoming - Journal of Medical Ethics.
    The exponential rise in transgender self-identification invites consideration of what constitutes an ethical response to transgender individuals’ claims about how best to promote their well-being. In this paper, we argue that ‘accepting’ a claim to medical transitioning in order to promote well-being would be in the person’s best interests iff at the point of request the individual is correct in their self-diagnosis as transgender such that the medical interventions they are seeking will help them to realise their preferences. If we (...)
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  16.  4
    Commentary on: 'Forever young? The ethics of ongoing puberty suppression for non-binary adults.Alessandra Lemma - 2020 - Journal of Medical Ethics Recent Issues 46 (11):757-758.
    Notini _et al_ 1 offer a timely addition in the wake of a significant increase in young people identifying as transgender and gender diverse. The authors focus specifically on the case of 18-year-old Phoenix’s request for ongoing puberty suppression to affirm a non-binary gender identity. A central issue raised by Phoenix’s predicament, and that I suggest we can extend to ethical consideration of requests for other types of medical intervention by binary and non-binary TGD individuals, is whether we should ‘affirm’ (...)
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  17.  6
    Commentary On: ‘Forever Young? The Ethics of Ongoing Puberty Suppression for Non-Binary Adults’.Alessandra Lemma - 2020 - Journal of Medical Ethics 46 (11):757-758.
    Notini et al 1 offer a timely addition in the wake of a significant increase in young people identifying as transgender and gender diverse. The authors focus specifically on the case of 18-year-old Phoenix’s request for ongoing puberty suppression to affirm a non-binary gender identity. A central issue raised by Phoenix’s predicament, and that I suggest we can extend to ethical consideration of requests for other types of medical intervention by binary and non-binary TGD individuals, is whether we should ‘affirm’ (...)
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  18.  2
    Der schwarze Spiegel.Alessandra Lemma - 2019 - Psyche 73 (9):644-672.
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  19.  13
    Inconsistency Lemmas in Algebraic Logic.James G. Raftery - 2013 - Mathematical Logic Quarterly 59 (6):393-406.
  20.  4
    Hidden Lemmas in Euler's Summation of the Reciprocals of the Squares.Curtis Tuckey & Mark McKinzie - 1997 - Archive for History of Exact Sciences 51 (1):29-57.
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  21.  8
    A Lemma in the Logic of Action.Timothy J. Surendonk - 1990 - Notre Dame Journal of Formal Logic 31 (2):222-224.
  22.  5
    False Lemmas in Herbrand.Burton Dreben & Peter Andrews - 1966 - Journal of Symbolic Logic 31 (4):657-659.
  23.  7
    A Lemma Concerning Recursive Functions and Its Applications.A. Mostowski - 1954 - Journal of Symbolic Logic 19 (4):299-300.
  24. Zorn's Lemma and Complete Boolean Algebras in Intuitionistic Type Theories.J. L. Bell - 1997 - Journal of Symbolic Logic 62 (4):1265-1279.
    We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. We also establish the persistence of some familiar results in the theory of Boolean algebras--notably, the proposition that every complete Boolean algebra is an absolute (...)
     
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  25.  9
    A Lemma for Cost Attained.Greg Hjorth - 2006 - Annals of Pure and Applied Logic 143 (1-3):87-102.
    A treeable ergodic equivalence relation of integer cost is generated by a free action of the free group on the corresponding number of generators. Every countable treeable ergodic equivalence relation is induced by the free action of some countable group.
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  26.  15
    Lemma Theory and Aphasiology.Carlo Semenza, Claudio Luzzatti & Sara Mondini - 1999 - Behavioral and Brain Sciences 22 (1):56-56.
    Recent aphasiological findings, not mentioned in the target article, have been accounted for by Levelt et al.'s theory and have, in turn, provided it with empirical support and new leads. This interaction is especially promising in the domain of complex word retrieval. Examples of particular categories of compounds are discussed.
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  27.  38
    Weak König's Lemma Implies Brouwer's Fan Theorem: A Direct Proof.Hajime Ishihara - 2006 - Notre Dame Journal of Formal Logic 47 (2):249-252.
    Classically, weak König's lemma and Brouwer's fan theorem for detachable bars are equivalent. We give a direct constructive proof that the former implies the latter.
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  28.  39
    A Lemma From Nowhere.Imogen Dickie - 2020 - Critica 52 (154).
    This paper uses cases involving empty singular terms to argue for a claim about the goal of ordinary belief-forming activity, and shows how this claim generates new foundations for the theory of reference.
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  29.  7
    Priming of Conflicting Motivational Orientations in Heavy Drinkers: Robust Effects on Self-Report but Not Implicit Measures.Lisa C. G. Di Lemma, Joanne M. Dickson, Pawel Jedras, Anne Roefs & Matt Field - 2015 - Frontiers in Psychology 6.
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  30.  1
    On Lemmas 1 and 2 to Proposition 39 of Book 3 of Newtons Principia.Geoffrey J. Dobson - 2001 - Archive for History of Exact Sciences 55 (4):345-363.
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  31.  8
    On Farkas' Lemma and Related Propositions in BISH.Josef Berger & Gregor Svindland - 2022 - Annals of Pure and Applied Logic 173 (2):103059.
    In this paper we analyse in the framework of constructive mathematics (BISH) the validity of Farkas' lemma and related propositions, namely the Fredholm alternative for solvability of systems of linear equations, optimality criteria in linear programming, Stiemke's lemma and the Superhedging Duality from mathematical finance, and von Neumann's minimax theorem with application to constructive game theory.
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  32. The Covering Lemma Up to a Woodin Cardinal.William Mitchell, Ernest Schimmerling & John Steel - 2003 - Bulletin of Symbolic Logic 9 (3):414-416.
     
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  33.  46
    A Case for the Lemma/Lexeme Distinction in Models of Speaking: Comment on Caramazza and Miozzo (1997).Ardi Roelofs, Antje S. Meyer & Willem J. M. Levelt - 1998 - Cognition 69 (2):219-230.
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  34.  19
    Rado Selection Lemma and Other Combinatorial Statements Uniformly Proved.Adam Kolany - 2005 - Bulletin of the Section of Logic 34 (3):143-149.
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  35. König's Lemma, the Ω-Rule and Primitive Recursive Arithmetic.E. G. K. López-Escobar - 1985 - Archive for Mathematical Logic 25 (1):67-74.
     
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  36. Note on a Lemma of Komori.Lloyd Humberstone - unknown
     
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  37.  27
    Complementary Lemmas in the Theory of Binary Relations.Raymond H. Burros - 1977 - Theory and Decision 8 (3):299-303.
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  38.  58
    Itô’s Lemma with Quantum Calculus : Some Implications. [REVIEW]Emmanuel Haven - 2011 - Foundations of Physics 41 (3):529-537.
    q-derivatives are part of so called quantum calculus. In this paper we investigate how such derivatives can possibly be used in Itô’s lemma. This leads us to consider how such derivatives can be used in a social science setting. We conclude that in a Itô Lemma setting we cannot use a macroscopic version of the Heisenberg uncertainty principle with q-derivatives.
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  39.  9
    Variations of Rado's Lemma.Paul Howard - 1993 - Mathematical Logic Quarterly 39 (1):353-356.
    The deductive strengths of three variations of Rado's selection lemma are studied in set theory without the axiom of choice. Two are shown to be equivalent to Rado's lemma and the third to the Boolean prime ideal theorem. MSC: 03E25, 04A25, 06E05.
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  40. The Diagonalization Lemma, Rosser and Tarski.Peter Smith - unknown
    We’ve now proved our key version of the First Theorem, Theorem 42. If T is the right kind of ω-consistent theory including enough arithmetic, then there will be an arithmetic sentence GT such that T ￿ GT and T ￿ ¬GT. Moreover, GT is constructed so that it is true if and only if unprovable-in T (so it is true). Now recall that, for a p.r. axiomatized theory T , Prf T(m, n) is the relation which holds just if m (...)
     
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  41.  11
    Ehrenfeucht’s Lemma in Set Theory.Gunter Fuchs, Victoria Gitman & Joel David Hamkins - 2018 - Notre Dame Journal of Formal Logic 59 (3):355-370.
    Ehrenfeucht’s lemma asserts that whenever one element of a model of Peano arithmetic is definable from another, they satisfy different types. We consider here the analogue of Ehrenfeucht’s lemma for models of set theory. The original argument applies directly to the ordinal-definable elements of any model of set theory, and, in particular, Ehrenfeucht’s lemma holds fully for models of set theory satisfying V=HOD. We show that the lemma fails in the forcing extension of the universe by (...)
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  42. Gettier Cases Without False Lemmas?Michael Levin - 2006 - Erkenntnis 64 (3):381-392.
    Examples cited by Feldman, Lehrer and others of true beliefs that are justified, but not by false lemmas, turn out under scrutiny to involve false lemmas after all. In each case there is an EG inference whose conclusion is unwarranted unless its base instance is false. A shift to non-deductive justification does not avert the difficulty. The relation of this result to non-inferential Gettier cases is suggested.
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  43. Rasiowa-Sokorski Lemma and Kripke Completeness of Predicate and Infinitary Modal Logics.Yoshihito Tanaka & Hiroakira Ono - 2000 - In Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 2. CSLI Publications. pp. 419-437.
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  44. Jónsson's Lemma for Regular and Nilpotent Shifts of Pseudovarieties.E. Graczynska & I. Chajda - 1997 - Bulletin of the Section of Logic 26 (2).
     
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  45.  11
    König's Infinity Lemma and Beth's Tree Theorem.George Weaver - 2017 - History and Philosophy of Logic 38 (1):48-56.
    König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite tree with (...)
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  46.  13
    Dickson’s Lemma and Weak Ramsey Theory.Yasuhiko Omata & Florian Pelupessy - 2019 - Archive for Mathematical Logic 58 (3-4):413-425.
    We explore the connections between Dickson’s lemma and weak Ramsey theory. We show that a weak version of the Paris–Harrington principle for pairs in c colors and miniaturized Dickson’s lemma for c-tuples are equivalent over \. Furthermore, we look at a cascade of consequences for several variants of weak Ramsey’s theorem.
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  47. Gilt Das Lemma von König „Konstruktiv “?Peter Zahn - 1985 - Archive for Mathematical Logic 25 (1):33-35.
     
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  48. Zorn's Lemma and Complete Boolean Algebras in Intuitionistic Type Theories.J. L. Bell - 1997 - Journal of Symbolic Logic 62 (4):1265-1279.
    We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. (Observe that the axiom of choice cannot be persistent in this sense since it implies the law of excluded middle.) We also establish the persistence (...)
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  49.  21
    The Weak König Lemma and Uniform Continuity.Josef Berger - 2008 - Journal of Symbolic Logic 73 (3):933-939.
    We prove constructively that the weak König lemma and quantifier-free number-number choice imply that every pointwise continuous function from Cantor space into Baire space has a modulus of uniform continuity.
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  50.  39
    On the Diagonal Lemma of Gödel and Carnap.Saeed Salehi - 2020 - Bulletin of Symbolic Logic 26 (1):80-88.
    A cornerstone of modern mathematical logic is the diagonal lemma of Gödel and Carnap. It is used in e.g. the classical proofs of the theorems of Gödel, Rosser and Tarski. From its first explication in 1934, just essentially one proof has appeared for the diagonal lemma in the literature; a proof that is so tricky and hard to relate that many authors have tried to avoid the lemma altogether. As a result, some so called diagonal-free proofs have (...)
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