Results for 'diagonalization of length continuum'

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  1.  29
    Almost Disjoint Families and Diagonalizations of Length Continuum.Dilip Raghavan - 2010 - Bulletin of Symbolic Logic 16 (2):240 - 260.
    We present a survey of some results and problems concerning constructions which require a diagonalization of length continuum to be carried out, particularly constructions of almost disjoint families of various sorts. We emphasize the role of cardinal invariants of the continuum and their combinatorial characterizations in such constructions.
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  2.  9
    The Length of Some Diagonalization Games.Marion Scheepers - 1999 - Archive for Mathematical Logic 38 (2):103-122.
    For X a separable metric space and $\alpha$ an infinite ordinal, consider the following three games of length $\alpha$ : In $G^{\alpha}_1$ ONE chooses in inning $\gamma$ an $\omega$ –cover $O_{\gamma}$ of X; TWO responds with a $T_{\gamma}\in O_{\gamma}$ . TWO wins if $\{T_{\gamma}:\gamma<\alpha\}$ is an $\omega$ –cover of X; ONE wins otherwise. In $G^{\alpha}_2$ ONE chooses in inning $\gamma$ a subset $O_{\gamma}$ of ${\sf C}_p(X)$ which has the zero function $\underline{0}$ in its closure, and TWO responds with a (...)
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  3. Where Α and Range Over Choice Sequences of Natural Numbers, M and X Over Natural Numbers, and Αm Stands for〈 Α (0), Α (1),..., Α (M− 1)〉, the Initial Segment of Α of Length M. An Immediate Consequence of WC-N is That All Full Functions Are Contin-Uous, and, as a Corollary, That the Continuum is Unsplittable [28]. Note That. [REVIEW]Mark van Atten & Dirk van Dalen - 2002 - Bulletin of Symbolic Logic 8 (3).
  4.  9
    Rehabilitation Services Following Total Joint Replacement: A Qualitative Analysis of Key Processes and Structures to Decrease Length of Stay and Increase Surgical Volumes in Ontario, Canada.Carol Fancott, Susan Jaglal, Victoria Quan, Katherine Berg, Cheryl A. Cott, Aileen Davis, John Flannery, Gillian Hawker, Michel D. Landry, Nizar N. Mahomed & Elizabeth Badley - 2010 - Journal of Evaluation in Clinical Practice 16 (4):724-730.
  5. Aristotle and Modern Mathematical Theories of the Continuum.Anne Newstead - 2001 - In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang.
    This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open (...)
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  6. On the Reality of the Continuum Discussion Note: A Reply to Ormell, ‘Russell's Moment of Candour’, Philosophy: Anne Newstead and James Franklin.Anne Newstead - 2008 - Philosophy 83 (1):117-127.
    In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding as (...)
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  7.  29
    Experience and Content: Consequences of a Continuum Theory.W. M. Davies - 1996 - Avebury.
    This book is about experiential content: what it is; what kind of account can be given of it. I am concerned with identifying and attacking one main view - I call it the inferentialist proposal. This account is central to the philosophy of mind, epistemology and philosophy of science and perception. I claim, however, that it needs to be recast into something far more subtle and enriched, and I attempt to provide a better alternative in these pages. The inferentialist proposal (...)
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  8.  15
    Subjective Averaging of Length with Serial Presentation.David J. Weiss & Norman H. Anderson - 1969 - Journal of Experimental Psychology 82 (1p1):52.
  9. The Logic and Topology of Kant's Temporal Continuum.Riccardo Pinosio & Michiel van Lambalgen - manuscript
    In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s (...)
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  10.  40
    Weak Forms of the Axiom of Choice and the Generalized Continuum Hypothesis.Arthur L. Rubin & Jean E. Rubin - 1993 - Mathematical Logic Quarterly 39 (1):7-22.
    In this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.
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  11.  54
    Distance and an Illusion of Length of Line.Frank Restle & Coleman Merryman - 1969 - Journal of Experimental Psychology 81 (2):297.
  12.  99
    Is the Dream Solution of the Continuum Hypothesis Attainable?Joel David Hamkins - 2015 - Notre Dame Journal of Formal Logic 56 (1):135-145.
    The dream solution of the continuum hypothesis would be a solution by which we settle the continuum hypothesis on the basis of a newly discovered fundamental principle of set theory, a missing axiom, widely regarded as true. Such a dream solution would indeed be a solution, since we would all accept the new axiom along with its consequences. In this article, however, I argue that such a dream solution to $\mathrm {CH}$ is unattainable.
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  13.  31
    Parameters of Paired-Associate Verbal Learning: Length of List, Meaningfulness, Rate of Presentation, and Ability.John B. Carroll & Mary Long Burke - 1965 - Journal of Experimental Psychology 69 (6):543.
  14.  28
    Major Elective Joint Replacement Surgery: Socioeconomic Variations in Surgical Risk, Postoperative Morbidity and Length of Stay.Jennifer Hollowell, Mike P. W. Grocott, Rebecca Hardy, Fares S. Haddad, Monty G. Mythen & Rosalind Raine - 2010 - Journal of Evaluation in Clinical Practice 16 (3):529-538.
  15.  39
    The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672-1686.Massimo Mugnai - 2003 - The Leibniz Review 13:155-165.
    This book consists of four parts: 1) an introduction of about 60 pages, mainly focused on the problem of the continuum in Leibniz; 2) a selection of Leibniz’s papers according to the critical edition prepared in Berlin, with English translation; 3) two appendices with excerpts in English from Leibniz’s papers and from texts of other authors on the continuum; 4) a rich collection of notes and a Latin-English glossary. In what follows I will make some short remarks about (...)
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  16.  8
    Test of Stimulus Sampling Theory for a Continuum of Responses with Unimodal Noncontingent Determinate Reinforcement.Patrick Suppes & Raymond W. Frankmann - 1961 - Journal of Experimental Psychology 61 (2):122.
  17.  13
    Amount of Training, Deprivation, and Variability of Chain Length as Determinants of Response-Velocity Gradients in Homogeneous Chains.John R. Platt - 1972 - Journal of Experimental Psychology 92 (2):191-197.
  18.  13
    List Length and Method of Presentation in Verbal Discrimination Learning with Further Evidence on Retroaction.Benton J. Underwood, John J. Shaughnessy & Joel Zimmerman - 1972 - Journal of Experimental Psychology 93 (1):181.
  19.  19
    Magnitude Estimation of Average Length and Average Inclination.Arthur L. Miller & Richard Sheldon - 1969 - Journal of Experimental Psychology 81 (1):16.
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  20.  17
    Length of Stay as Risk Factor for Inappropriate Hospital Days: Interaction with Patient Age and Co‐Morbidity.Riccardo Barisonzo, Wolfgang Wiedermann, Matthias Unterhuber & Christian J. Wiedermann - 2013 - Journal of Evaluation in Clinical Practice 19 (1):80-85.
  21. Weyl's Conception of the Continuum in a Husserlian Transcendental Perspective.Stathis Livadas - 2017 - Studia Philosophica Estonica 10 (1):99-124.
    This article attempts to broaden the phenomenologically motivated perspective of H. Weyl's Das Kontinuum in the hope of elucidating the differences between the intuitive and mathematical continuum and further providing a deeper phenomenological interpretation. It is known that Weyl sought to develop an arithmetically based theory of continuum with the reasoning that one should be based on the naturally accessible domain of natural numbers and on the classical first-order predicate calculus to found a theory of mathematical continuum (...)
     
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  22.  11
    Remote Associations as a Function of the Length of Interval Between Learning and Recall.J. T. Wilson - 1943 - Journal of Experimental Psychology 33 (1):40.
  23.  10
    Short-Term Retention of Sequentially Presented Digits as a Function of Interdigit Interval, Digit Duration, and Series Length.Thomas E. Sitterley - 1968 - Journal of Experimental Psychology 78 (1):174.
  24.  9
    Dissipation of Sensory Aftereffects as a Function of Axon Length.George Singer & John K. Collins - 1972 - Journal of Experimental Psychology 96 (1):194.
  25.  6
    The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672-1686. [REVIEW]Massimo Mugnai - 2003 - The Leibniz Review 13:155-165.
    This book consists of four parts: 1) an introduction of about 60 pages, mainly focused on the problem of the continuum in Leibniz; 2) a selection of Leibniz’s papers according to the critical edition prepared in Berlin, with English translation; 3) two appendices with excerpts in English from Leibniz’s papers and from texts of other authors on the continuum; 4) a rich collection of notes and a Latin-English glossary. In what follows I will make some short remarks about (...)
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  26.  11
    Effect of Amount of Interpolated Learning and Length of Retention Interval Upon Retroactive Inhibition in a Serial Search Task.Robert E. Hicks & Robert K. Young - 1973 - Journal of Experimental Psychology 100 (2):297.
  27.  9
    Resistance to Extinction as a Joint Function of Partial Reward Pattern and Length of Training.Neal E. Grossen - 1969 - Journal of Experimental Psychology 79 (2p1):385.
  28.  10
    Effects of Interstimulus Interval Length and Variability on Habituation of Autonomic Components of the Orienting Response.Robert J. Gatchel & Peter J. Lang - 1974 - Journal of Experimental Psychology 103 (4):802.
  29.  3
    Motor Performance on Temporal Tasks as a Function of Sequence Length and Coherence.Don Trumbo, Merrill Noble, Frank Fowler & James Porterfield - 1968 - Journal of Experimental Psychology 77 (3p1):397.
  30.  1
    The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672-1686.Massimo Mugnai - 2003 - The Leibniz Review 13:155-165.
    This book consists of four parts: 1) an introduction of about 60 pages, mainly focused on the problem of the continuum in Leibniz; 2) a selection of Leibniz’s papers according to the critical edition prepared in Berlin, with English translation; 3) two appendices with excerpts in English from Leibniz’s papers and from texts of other authors on the continuum; 4) a rich collection of notes and a Latin-English glossary. In what follows I will make some short remarks about (...)
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  31. On the Reality of the Continuum Discussion Note: A Reply to Ormell, 'Russell's Moment of Candour', "Philosophy".Anne Newstead & James Franklin - 2008 - Philosophy 83 (1):117-127.
    This paper discusses an argument for the reality of the classical mathematical continuum. An inference to the best explanation type of argument is used to defend the idea that real numbers exist even when they cannot be constructively specified as with the "indefinable numbers".
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  32.  17
    Cardinal Invariants of the Continuum and Combinatorics on Uncountable Cardinals.Jörg Brendle - 2006 - Annals of Pure and Applied Logic 144 (1):43-72.
    We explore the connection between combinatorial principles on uncountable cardinals, like stick and club, on the one hand, and the combinatorics of sets of reals and, in particular, cardinal invariants of the continuum, on the other hand. For example, we prove that additivity of measure implies that Martin’s axiom holds for any Cohen algebra. We construct a model in which club holds, yet the covering number of the null ideal is large. We show that for uncountable cardinals κ≤λ and (...)
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  33.  29
    How to Define a Unit of Length.Jakub Mácha - forthcoming - 9th National Conference of the Italian Society for Analytic Philosophy. Truth, Knowledge, and Science, 2010.
    In this paper, I shall discuss the issue whether the standard meter in Paris is in fact one meter long. Whether one could meaningfully assert this proposition depends on how the unit of length a meter is defined. I would like to suggest three conceivable definitions. One meter long is everything that has the same length as an arbitrary chosen rod S now has. According to the second definition one meter long is everything that coincides in the endpoints (...)
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  34.  20
    Cardinal Invariants and the Collapse of the Continuum by Sacks Forcing.Miroslav Repický - 2008 - Journal of Symbolic Logic 73 (2):711 - 727.
    We study cardinal invariants of systems of meager hereditary families of subsets of ω connected with the collapse of the continuum by Sacks forcing S and we obtain a cardinal invariant yω such that S collapses the continuum to yω and y ≤ yω ≤ b. Applying the Baumgartner-Dordal theorem on preservation of eventually narrow sequences we obtain the consistency of y = yω < b. We define two relations $\leq _{0}^{\ast}$ and $\leq _{1}^{\ast}$ on the set $(^{\omega}\omega)_{{\rm (...)
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  35.  5
    Games of Length Ω1.Itay Neeman - 2007 - Journal of Mathematical Logic 7 (1):83-124.
    We prove determinacy for open length ω1 games. Going further we introduce, and prove determinacy for, a stronger class of games of length ω1, with payoff conditions involving the entire run, the club filter on ω1, and a sequence of ω1 disjoint stationary subsets of ω1. The determinacy proofs use an iterable model with a class of indiscernible Woodin cardinals, and we show that the games precisely capture the theory of the minimal model for this assumption.
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  36.  27
    The Origins of Length Contraction: I. The Fitzgerald-Lorentz Deformation Hypothesis.Harvey R. Brown - 2001 - American Journal of Physics 69:1044-1054.
    One of the widespread confusions concerning the history of the 1887 Michelson-Morley experiment has to do with the initial explanation of this celebrated null result due independently to FitzGerald and Lorentz. In neither case was a strict, longitudinal length contraction hypothesis invoked, as is commonly supposed. Lorentz postulated, particularly in 1895, any one of a certain family of possible deformation effects for rigid bodies in motion, including purely transverse alteration, and expansion as well as contraction; FitzGerald may well have (...)
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  37.  18
    The Continuing Continuum Problem of Deposits and Loans.Philipp Bagus & David Howden - 2012 - Journal of Business Ethics 106 (3):295-300.
    Barnett and Block (J Bus Ethics 18(2):179–194, 2011 ) argue that one cannot distinguish between deposits and loans due to the continuum problem of maturities and because future goods do not exist—both essential characteristics that distinguish deposit from loan contracts. In a similar way but leading to opposite conclusions (Cachanosky, forthcoming) maintains that both maturity mismatching and fractional reserve banking are ethically justified as these contracts are equivalent. We argue herein that the economic and legal differences between genuine deposit (...)
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  38. Phenomenological Architecture of a Mind and Operational Architectonics of the Brain: The Unified Metastable Continuum.Andrew A. Fingelkurts, Alexander A. Fingelkurts & Carlos F. H. Neves - 2009 - In Robert Kozma & John Caulfield (eds.), Journal of New Mathematics and Natural Computing. Special Issue on Neurodynamic Correlates of Higher Cognition and Consciousness: Theoretical and Experimental Approaches - in Honor of Walter J Freeman's 80th Birthday. World Scientific. pp. 221-244.
    In our contribution we will observe phenomenal architecture of a mind and operational architectonics of the brain and will show their intimate connectedness within a single integrated metastable continuum. The notion of operation of different complexity is the fundamental and central one in bridging the gap between brain and mind: it is precisely by means of this notion that it is possible to identify what at the same time belongs to the phenomenal conscious level and to the neurophysiological level (...)
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  39. From Panexperientialism to Conscious Experience: The Continuum of Experience.Gregory M. Nixon - 2010 - Journal of Consciousness Exploration and Research 1 (3):216-233.
    When so much is being written on conscious experience, it is past time to face the question whether experience happens that is not conscious of itself. The recognition that we and most other living things experience non-consciously has recently been firmly supported by experimental science, clinical studies, and theoretic investigations; the related if not identical philosophic notion of experience without a subject has a rich pedigree. Leaving aside the question of how experience could become conscious of itself, I aim here (...)
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  40. The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672-1686.Richard T. W. Arthur (ed.) - 2001 - Yale University Press.
    This book gathers together for the first time an important body of texts written between 1672 and 1686 by the great German philosopher and polymath Gottfried Leibniz. These writings, most of them previously untranslated, represent Leibniz’s sustained attempt on a problem whose solution was crucial to the development of his thought, that of the composition of the continuum. The volume begins with excerpts from Leibniz’s Paris writings, in which he tackles such problems as whether the infinite division of matter (...)
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  41.  5
    The Leap From the Ego of Temporal Consciousness to the Phenomenology of Mathematical Continuum.Stathis Livadas - 2009 - Manuscrito 32 (2):321-356.
    This article attempts to link the notion of absolute ego as the ultimate subjectivity of consciousness in continental tradition with a phenomenology of Mathematical Continuum as this term is generally established following Cantor’s pioneering ideas on the properties and cardinalities of sets. My motivation stems mainly from the inherent ambiguities underlying the nature and properties of this fundamental mathematical notion which, in my view, cannot be resolved in principle by the analytical means of any formal language not even by (...)
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  42.  20
    Klein Paradox for the Bosonic Equation in the Presence of Minimal Length.M. Falek, M. Merad & M. Moumni - 2015 - Foundations of Physics 45 (5):507-524.
    We present an exact solution of the one-dimensional modified Klein Gordon and Duffin Kemmer Petiau equations with a step potential in the presence of minimal length in the uncertainty relation, where the expressions of the new transmission and reflection coefficients are determined for all cases. As an application, the Klein paradox in the presence of minimal length is discussed for all equations.
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  43. Dynamical Interpretation of Leibniz’s Continuum.Vassil Vidinsky - 2008 - Kaygi 10:51-70.
    This dynamical interpretation of the continuum is based on a threefold perspective. First, detailed differentiation of all standard realms of Leibnizian Weltanschauung – (R real), (P phenomenal), (I ideal). Second, analysis of the scope of the Law of Continuity famously formulated by Leibniz and mapping it onto this (RPI) structure. Third, finding the precise place of dynamics and force in this (RPI) continuum.
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  44.  13
    The Ends of a Continuum: Genetic and Temperature-Dependent Sex Determination in Reptiles.Stephen D. Sarre, Arthur Georges & Alex Quinn - 2004 - Bioessays 26 (6):639-645.
    Two prevailing paradigms explain the diversity of sex-determining modes in reptiles. Many researchers, particularly those who study reptiles, consider genetic and environmental sex-determining mechanisms to be fundamentally different, and that one can be demonstrated experimentally to the exclusion of the other. Other researchers, principally those who take a broader taxonomic perspective, argue that no clear boundaries exist between them. Indeed, we argue that genetic and environmental sex determination in reptiles should be seen as a continuum of states represented by (...)
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  45.  57
    Intuition Between the Analytic-Continental Divide: Hermann Weyl's Philosophy of the Continuum.Janet Folina - 2008 - Philosophia Mathematica 16 (1):25-55.
    Though logical positivism is part of Kant's complex legacy, positivists rejected both Kant's theory of intuition and his classification of mathematical knowledge as synthetic a priori. This paper considers some lingering defenses of intuition in mathematics during the early part of the twentieth century, as logical positivism was born. In particular, it focuses on the difficult and changing views of Hermann Weyl about the proper role of intuition in mathematics. I argue that it was not intuition in general, but his (...)
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  46.  3
    Are We Closer to a Solution of the Continuum Problem?Carlos di Prisco - 2005 - Manuscrito 28 (2):331-350.
    The Continuum Hypothesis has motivated a considerable part of the development of axiomatic set theory for over a century. We present, in a very schematic way, some of the results that give information related to Cantor’s Continuum Problem.
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  47.  60
    Experience and Content: Consequences of a Continuum Theory.W. Martin Davies - 1993 - Dissertation,
    This thesis is about experiential content: what it is; what kind of account can be given of it. I am concerned with identifying and attacking one main view - I call it the inferentialist proposal. This account is central to the philosophy of mind, epistemology and philosophy of science and perception. I claim, however, that it needs to be recast into something far more subtle and enriched, and I attempt to provide a better alternative in these pages. The inferentialist proposal (...)
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  48. Discrete or Continuous? The Quest for Fundamental Length in Modern Physics.Amit Hagar - 2014 - Cambridge University Press.
    A book on the notion of fundamental length, covering issues in the philosophy of math, metaphysics, and the history and the philosophy of modern physics, from classical electrodynamics to current theories of quantum gravity. Published (2014) in Cambridge University Press.
  49.  20
    A Hierarchy of Tree-Automatic Structures.Olivier Finkel & Stevo Todorčević - 2012 - Journal of Symbolic Logic 77 (1):350-368.
    We consider ω n -automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length ω n for some integer n ≥ 1. We show that all these structures are ω-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation for ω 2 -automatic (resp. ω n -automatic for n > 2) boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups) is (...)
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  50.  27
    Creature Forcing and Large Continuum: The Joy of Halving.Jakob Kellner & Saharon Shelah - 2012 - Archive for Mathematical Logic 51 (1-2):49-70.
    For ${f,g\in\omega^\omega}$ let ${c^\forall_{f,g}}$ be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let ${c^\exists_{f,g}}$ be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that it is consistent that ${c^\exists_{f_\epsilon,g_\epsilon}{=}c^\forall_{f_\epsilon,g_\epsilon}{=}\kappa_\epsilon}$ for continuum many pairwise different cardinals ${\kappa_\epsilon}$ and suitable pairs ${(f_\epsilon,g_\epsilon)}$ . For the proof we introduce a new mixed-limit creature (...)
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