Results for 'cardinal invariants of the continuum'

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  1.  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 (...)
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  2.  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 (...)
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  3.  8
    Ideals Over Ω and Cardinal Invariants of the Continuum.P. Matet & J. Pawlikowski - 1998 - Journal of Symbolic Logic 63 (3):1040-1054.
    Let P be any one of the following combinatorial properties: weak P-pointness, weak (semi-) Q-pointness, weak (semi-)selectivity, ω-closedness. We deal with the following two questions: (1) What is the least cardinal κ such that there exists an ideal with κ many generators that does not have the property P? (2) Can one extend every ideal with the property P to a prime ideal with the property P?
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  4.  12
    S. Shelah. On Cardinal Invariants of the Continuum. Axiomatic Set Theory, Translated and Edited by D. A. Martin, J. Baumgartner, and S. Shelah, Contemporary Mathematics, Vol. 31. American Mathematical Society, Providence, 1984, Pp. 183–207. [REVIEW]Juris Steprāns - 2005 - Bulletin of Symbolic Logic 11 (3):451-453.
  5. On Cardinal Invariants of the Continuum. Axiomatic Set Theory.S. Shelah, D. A. Martin & J. Baumgartner - 2005 - Bulletin of Symbolic Logic 11 (3):451-453.
     
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  6. REVIEWS-On Cardinal Invariants of the Continuum.S. Shelah & Juris Steprans - 2005 - Bulletin of Symbolic Logic 11 (3):451-453.
     
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  7.  82
    Pair-Splitting, Pair-Reaping and Cardinal Invariants of F Σ -Ideals.Michael Hrušák, David Meza-Alcántara & Hiroaki Minami - 2010 - Journal of Symbolic Logic 75 (2):661-677.
    We investigate the pair-splitting number $\germ{s}_{pair}$ which is a variation of splitting number, pair-reaping number $\germ{r}_{pair}$ which is a variation of reaping number and cardinal invariants of ideals on ω. We also study cardinal invariants of F σ ideals and their upper bounds and lower bounds. As an application, we answer a question of S. Solecki by showing that the ideal of finitely chromatic graphs is not locally Katětov-minimal among ideals not satisfying Fatou's lemma.
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  8.  19
    Cardinal Invariants Above the Continuum.James Cummings & Saharon Shelah - 1995 - Annals of Pure and Applied Logic 75 (3):251-268.
    We prove some consistency results about and δ, which are natural generalisations of the cardinal invariants of the continuum and . We also define invariants cl and δcl, and prove that almost always = cl and = cl.
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  9.  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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  10. The Cofinality of the Infinite Symmetric Group and Groupwise Density.Jörg Brendle & Maria Losada - 2003 - Journal of Symbolic Logic 68 (4):1354-1361.
    We show that g ≤ c(Sym(ω)) where g is the groupwise density number and c(Sym(ω)) is the cofinality of the infinite symmetric group. This solves (the second half of) a problem addressed by Thomas.
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  11.  26
    Changing Cardinal Invariants of the Reals Without Changing Cardinals or the Reals.Heike Mildenberger - 1998 - Journal of Symbolic Logic 63 (2):593-599.
    We show: The procedure mentioned in the title is often impossible. It requires at least an inner model with a measurable cardinal. The consistency strength of changing b and d from a regular κ to some regular δ < κ is a measurable of Mitchell order δ. There is an application to Cichon's diagram.
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  12.  36
    Cardinal Coefficients Associated to Certain Orders on Ideals.Piotr Borodulin-Nadzieja & Barnabás Farkas - 2012 - Archive for Mathematical Logic 51 (1-2):187-202.
    We study cardinal invariants connected to certain classical orderings on the family of ideals on ω. We give topological and analytic characterizations of these invariants using the idealized version of Fréchet-Urysohn property and, in a special case, using sequential properties of the space of finitely-supported probability measures with the weak* topology. We investigate consistency of some inequalities between these invariants and classical ones, and other related combinatorial questions. At last, we discuss maximality properties of almost disjoint (...)
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  13. The Cofinality of Cardinal Invariants Related to Measure and Category.Tomek Bartoszynski, Jaime I. Ihoda & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (3):719-726.
    We prove that the following are consistent with ZFC. 1. 2 ω = ℵ ω 1 + K C = ℵ ω 1 + K B = K U = ω 2 (for measure and category simultaneously). 2. 2 ω = ℵ ω 1 = K C (L) + K C (M) = ω 2 . This concludes the discussion about the cofinality of K C.
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  14.  14
    Some Cardinal Invariants of the Generalized Baire Spaces, Universität Wien, Austria, 2017. Supervised by Sy-David Friedman.Diana Carolina Montoya - 2018 - Bulletin of Symbolic Logic 24 (2):197-197.
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  15.  7
    The Nikodym Property and Cardinal Characteristics of the Continuum.Damian Sobota - 2019 - Annals of Pure and Applied Logic 170 (1):1-35.
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  16.  21
    Blass Andreas. Simple Cardinal Characteristics of the Continuum. Set Theory of the Reals, Edited by Judah Haim, Israel Mathematical Conference Proceedings, Vol. 6, Gelbart Research Institute for Mathematical Sciences, Bar-Ilan University, Ramat-Gan 1993, Distributed by the American Mathematical Society, Providence, Pp. 63–90. [REVIEW]Heike Mildenberger - 2002 - Bulletin of Symbolic Logic 8 (4):552-553.
  17.  5
    Review: Andreas Blass, Haim Judah, Simple Cardinal Characteristics of the Continuum[REVIEW]Heike Mildenberger - 2002 - Bulletin of Symbolic Logic 8 (4):552-553.
  18.  18
    Moti Gitik and Menachem Magidor. The Singular Cardinal Hypothesis Revisited. Set Theory of the Continuum, Edited by H. Judah, W. Just, and H. Woodin, Mathematical Sciences Research Institute Publications, Vol. 26, Springer-Verlag, New York Etc. 1992, Pp. 243–279. [REVIEW]James Cummings - 1995 - Journal of Symbolic Logic 60 (1):339-340.
  19.  5
    Review: K. Prikry, The Consistency of the Continuum Hypothesis for the First Measurable Cardinal[REVIEW]M. Boffa - 1973 - Journal of Symbolic Logic 38 (4):652-652.
  20.  1
    Příkrý K.. The Consistency of the Continuum Hypothesis for the First Measurable Cardinal. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques Et Physiques, Vol. 13 , Pp. 193–197. [REVIEW]M. Boffa - 1973 - Journal of Symbolic Logic 38 (4):652-652.
  21.  18
    Fred Appenzeller. An Independence Result in Quadratic Form Theory: Infinitary Combinatorics Applied to Ε-Hermitian Spaces. The Journal of Symbolic Logic, Vol. 54 , Pp. 689–699. - Otmar Spinas. Linear Topologies on Sesquilinear Spaces of Uncountable Dimension. Fundamenta Mathematicae, Vol. 139 , Pp. 119–132. - James E. Baumgartner, Matthew Foreman, and Otmar Spinas. The Spectrum of the Γ-Invariant of a Bilinear Space. Journal of Algebra, Vol. 189 , Pp. 406–418. - James E. Baumgartner and Otmar Spinas. Independence and Consistency Proofs in Quadratic Form Theory. The Journal of Symbolic Logic, Vol. 56 , Pp. 1195–1211. - Otmar Spinas. Iterated Forcing in Quadratic Form Theory. Israel Journal of Mathematics, Vol. 79 , Pp. 297–315. - Otmar Spinas. Cardinal Invariants and Quadratic Forms. Set Theory of the Reals, Edited by Haim Judah, Israel Mathematical Conference Proceedings, Vol. 6, Gelbart Research Institute for Mathematical Sciences, Bar-Ilan University, Ramat-Gan 1993, Distributed by T. [REVIEW]Paul C. Eklof - 2001 - Bulletin of Symbolic Logic 7 (2):285-286.
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  22.  52
    Intersection Numbers of Families of Ideals.M. Hrušák, C. A. Martínez-Ranero, U. A. Ramos-García & O. A. Téllez-Nieto - 2013 - Archive for Mathematical Logic 52 (3-4):403-417.
    We study the intersection number of families of tall ideals. We show that the intersection number of the class of analytic P-ideals is equal to the bounding number ${\mathfrak{b}}$ , the intersection number of the class of all meager ideals is equal to ${\mathfrak{h}}$ and the intersection number of the class of all F σ ideals is between ${\mathfrak{h}}$ and ${\mathfrak{b}}$ , consistently different from both.
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  23.  31
    Cardinal Invariants of Monotone and Porous Sets.Michael Hrušák & Ondřej Zindulka - 2012 - Journal of Symbolic Logic 77 (1):159-173.
    A metric space (X, d) is monotone if there is a linear order < on X and a constant c such that d(x, y) ≤ c d(x, z) for all x < y < z in X. We investigate cardinal invariants of the σ-ideal Mon generated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants (...)
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  24.  17
    Ordering MAD Families a la Katětov.Michael Hrušák & Salvador García Ferreira - 2003 - Journal of Symbolic Logic 68 (4):1337-1353.
    An ordering (≤K) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size.
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  25.  11
    Remarks on Gaps in Documentclass{Article}Usepackage{Amssymb}Begin{Document}Pagestyle{Empty}${Mathrm{Dense}(Mathbb {Q})/Mathbf {Nwd}}$End{Document}.Teppo Kankaanpää - 2013 - Mathematical Logic Quarterly 59 (1-2):51-61.
    The structure Dense /nwd and gaps in analytic quotients of equation image have been studied in the literature 2, 3, 1. We prove that the structures Dense /nwd and equation image have gaps of type equation image, and there are no -gaps for equation image, where equation image is the additivity number of the meager ideal. We also prove the existence of -gaps in these structures. Finally we characterize the cofinality of the meager ideal equation image using families of sets (...)
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  26.  53
    Around Splitting and Reaping for Partitions of Ω.Hiroaki Minami - 2010 - Archive for Mathematical Logic 49 (4):501-518.
    We investigate splitting number and reaping number for the structure (ω) ω of infinite partitions of ω. We prove that ${\mathfrak{r}_{d}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N}),\mathfrak{d}}$ and ${\mathfrak{s}_{d}\geq\mathfrak{b}}$ . We also show the consistency results ${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}$ and ${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})}$ . To prove the consistency ${\mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}$ and ${\mathfrak{s}_{d} < \mathsf{cof}(\mathcal{M})}$ we introduce new cardinal invariants ${\mathfrak{r}_{pair}}$ and ${\mathfrak{s}_{pair}}$ . We also study the relation between ${\mathfrak{r}_{pair}, \mathfrak{s}_{pair}}$ and other cardinal (...)
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  27.  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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  28.  47
    Isolating Cardinal Invariants.Jindřich Zapletal - 2003 - Journal of Mathematical Logic 3 (1):143-162.
    There is an optimal way of increasing certain cardinal invariants of the continuum.
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  29. 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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  30.  4
    On Two Topological Cardinal Invariants of an Order-Theoretic Flavour.Santi Spadaro - 2012 - Annals of Pure and Applied Logic 163 (12):1865-1871.
    Noetherian type and Noetherian π-type are two cardinal functions which were introduced by Peregudov in 1997, capturing some properties studied earlier by the Russian School. Their behavior has been shown to be akin to that of the cellularity, that is the supremum of the sizes of pairwise disjoint non-empty open sets in a topological space. Building on that analogy, we study the Noetherian π-type of κ-Suslin Lines, and we are able to determine it for every κ up to the (...)
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  31.  6
    Cardinal Invariants of Infinite Groups.Jörg Brendle - 1990 - Archive for Mathematical Logic 30 (3):155-170.
    LetG be a group. CallG akC-group if every element ofG has less thank conjugates. Denote byP(G) the least cardinalk such that any subset ofG of sizek contains two elements which commute.It is shown that the existence of groupsG such thatP(G) is a singular cardinal is consistent withZFC. So is the existence of groupsG which are notkC but haveP(G)cardinal. On the other hand, ifk is a singular strong limit cardinal, andG is akC-group, thenP(G)≠k. (...)
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  32.  4
    More on Cardinal Invariants of Boolean Algebras.Andrzej Rosłanowski & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):1-37.
    We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that . We prove consistency of the statement “there is a Boolean algebra such that ” and we force a superatomic Boolean algebra such that , and . Next we force a superatomic algebra such that and a superatomic algebra such that . Finally we show that consistently there is a Boolean algebra of (...)
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  33. 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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  34.  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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  35. 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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  36.  21
    Distributive Proper Forcing Axiom and Cardinal Invariants.Huiling Zhu - 2013 - Archive for Mathematical Logic 52 (5-6):497-506.
    In this paper, we study the forcing axiom for the class of proper forcing notions which do not add ω sequence of ordinals. We study the relationship between this forcing axiom and many cardinal invariants. We use typical iterated forcing with large cardinals and analyse certain property being preserved in this process. Lastly, we apply the results to distinguish several forcing axioms.
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  37. 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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  38.  74
    The Genesis of the Peircean Continuum.Matthew E. Moore - 2007 - Transactions of the Charles S. Peirce Society 43 (3):425 - 469.
    : In the Cambridge Conferences Lectures of 1898 Peirce defines a continuum as a "collection of so vast a multitude" that its elements "become welded into one another." He links the transinfinity (the "vast multitude") of a continuum to the confusion of its elements by a line of mathematical reasoning closely related to Cantor's Theorem. I trace the mathematical and philosophical roots of this conception of continuity, and examine its unresolved tensions, which arise mainly from difficulties in Peirce's (...)
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  39. 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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  40.  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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  41.  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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  42.  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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  43.  42
    An Approach to the Modelling of the Physical Continuum.Richard Jozsa - 1986 - British Journal for the Philosophy of Science 37 (4):395-404.
    We describe a way of constructing models for the continuum which does not require an underlying structure of points. With a condition of spatial homogeneity the models have the mathematical structure of a sheaf.
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  44. 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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  45. 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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  46. 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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  47.  23
    The Measure of All Gods: Religious Paradigms of the Antiquity as Anthropological Invariants.Alex V. Halapsis - 2018 - Anthropological Measurements of Philosophical Research 14:158-171.
    Purpose of the article is the reconstruction of ancient Greek and ancient Roman models of religiosity as anthropological invariants that determine the patterns of thinking and being of subsequent eras. Theoretical basis. The author applied the statement of Protagoras that "Man is the measure of all things" to the reconstruction of the religious sphere of culture. I proceed from the fact that each historical community has a set of inherent ideas about the principles of reality, which found unique "universes (...)
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  48.  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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  49.  40
    Continuous Bodies, Impenetrability, and Contact Interactions: The View From the Applied Mathematics of Continuum Mechanics.S. R. Smith - 2007 - British Journal for the Philosophy of Science 58 (3):503-538.
    Many philosophers have claimed that there is a tension between the impenetrability of matter and the possibility of contact between continuous bodies. This tension has led some to claim that impenetrable continuous bodies could not ever be in contact, and it has led others to posit certain structural features to continuous bodies that they believe would resolve the tension. Unfortunately, such philosophical discussions rarely borrow much from the investigation of actual matter. This is probably largely because actual matter is not (...)
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  50.  18
    Aronszajn Trees and Failure of the Singular Cardinal Hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
    The tree property at κ+ states that there are no Aronszajn trees on κ+, or, equivalently, that every κ+ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ+ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible above strongly compacts. In this paper, we reconcile the two. We (...)
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