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    Wyświetlanie 1-8 z 8
    Tytuł:
    On infinite partitions of lines and space
    Autorzy:
    Erdös, Paul
    Jackson, Steve
    Mauldin, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/1205459.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    transfinite recursion
    Martin's Axiom
    forcing
    geometry
    infinite partitions
    Opis:
    Given a partition P:L → ω of the lines in $ℝ^n$, n ≥ 2, into countably many pieces, we ask if it is possible to find a partition of the points, $Q:ℝ^n → ω$, so that each line meets at most m points of its color. Assuming Martin's Axiom, we show this is the case for m ≥ 3. We reduce the problem for m = 2 to a purely finitary geometry problem. Although we have established a very similar, but somewhat simpler, version of the geometry conjecture, we leave the general problem open. We consider also various generalizations of these results, including to higher dimension spaces and planes.
    Źródło:
    Fundamenta Mathematicae; 1997, 152, 1; 75-95
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The measure algebra does not always embed
    Autorzy:
    Dow, Alan
    Hart, Klaas
    Powiązania:
    https://bibliotekanauki.pl/articles/1205120.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    measure algebra
    embedding
    Open Colouring Axiom
    P(ℕ)/fin
    Opis:
    The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.
    Źródło:
    Fundamenta Mathematicae; 2000, 163, 2; 163-176
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundaries, Martins Axiom, and (P)-properties in dual Banach spaces
    Autorzy:
    Granero, Antonio S.
    Hernández, Juan M.
    Powiązania:
    https://bibliotekanauki.pl/articles/745016.pdf
    Data publikacji:
    2016
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Boundaries, Martin's Axiom, equality \(Seq(X^{**})=X^{**}\), super-(P) property
    Opis:
    Let \(X\) be a~Banach space and \(\mathcal{S} \mathit{eq}(X^{**})\) (resp., \(X_{\aleph_0}\)) the subset of elements \(\psi\in X^{**}\) such that there exists a~sequence \((x_n)_{n\geq 1}\subset X\) such that \(x_n\to \psi\) in the \(w^*\)-topology of \(X^{**}\) (resp., there exists a~separable subspace \(Y\subset X\) such that \(\psi\in \smash{{\overline{Y}^{w^*}}}\)). Then: (i) if \(\operatorname{Dens}(X)\geq \aleph _1\), the property \(X^{**}=X_{\aleph _0}\) (resp., \(X^{**}=\mathcal{S}\mathit{eq}(X^{**})\)) is \(\aleph _1\)-determined, i.e., \(X\)~has this property iff \(Y\) has, for every subspace \(Y\subset X\) with \(\operatorname{Dens}(Y)=\aleph _1\); (ii) if \(X^{**}=X _{\aleph _0}\), \( (B(X^{**}),w^*)\) has countable tightness; (iii) under the Martin's axiom \(\mathit{MA} (\omega _1)\) we have \(X^{**}=\mathcal{S}\mathit{eq}(X^{**})\) iff \((B(X^*),w^*)\) has countable tightness and \(\\overline {\text {co}}(B)=\overline {\text {co}} ^{w^*}(K)\) for every subspace \(Y\subset X\), every \(w^*\)-compact subset \(K\) of \(Y^*\), and every boundary \(B\subset K\).
    Źródło:
    Commentationes Mathematicae; 2016, 56, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sociology of/as Culture The Unfinished Methodology of Florian Znaniecki
    Autorzy:
    Lueschen, Gunther
    Powiązania:
    https://bibliotekanauki.pl/articles/1929434.pdf
    Data publikacji:
    2007-09-21
    Wydawca:
    Polskie Towarzystwo Socjologiczne
    Tematy:
    cultural reality
    cultural sciences
    methodology
    system theory
    Vico-Axiom
    analytic induction
    Opis:
    While Florian Znaniecki’s work is best known through his joint work with William I. Thomas on The Polish Peasant in Europe and America, his most important work deals with the methodology and substance of sociology of culture, based on three origins: systems theory, the identification of cultural science along the Vico-Axiom (his culturalism), and his cultural realism. Of the major sources of specific sociology of culture, he analyses in The Method of Sociology (1934) as a system approach, types of cultural and sociological data, existing methodological tendencies and the development of analytic induction which means a conglomerate of logic principles and a principle based on exception rather than the rule of insight. His final work Cultural Sciences (1952) is an attempt to include data and their interpretation from a set of cultural sciences, whereby the functionality of sociology as a cultural specialty is increasing the sociologists specialize in the comparative studies of other cultural sciences.
    Źródło:
    Polish Sociological Review; 2007, 158, 2; 209-222
    1231-1413
    2657-4276
    Pojawia się w:
    Polish Sociological Review
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Presentation of Mathematical Induction by Formula of Algebra of Algorithms
    Autorzy:
    Ovsyak, V.
    Ovsyak, O.
    Petrushka, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/114070.pdf
    Data publikacji:
    2016
    Wydawca:
    Stowarzyszenie Inżynierów i Techników Mechaników Polskich
    Tematy:
    formula of the axiom of mathematical induction
    tautology
    truthful formula
    ordering of the variable values
    Opis:
    The analysis of the axiom of mathematical induction, which is given by the formula of mathematical logics is presented in the paper. It has been established that the famous formula of mathematical induction is executed only in case of ordered values of the variable linked by a quantifier. This ordering is not described analytically. Algebra of algorithms is applied for an analytical description of ordering of the variable values. The axiom of mathematical induction is described by the formula of algebra of algorithms.
    Źródło:
    Measurement Automation Monitoring; 2016, 62, 11; 367-370
    2450-2855
    Pojawia się w:
    Measurement Automation Monitoring
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    What are the limits of mathematical explanation? Interview with Charles McCarty by Piotr Urbańczyk
    Autorzy:
    McCarty, David Charles
    Urbańczyk, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/691211.pdf
    Data publikacji:
    2016
    Wydawca:
    Copernicus Center Press
    Tematy:
    mathematics
    logic
    mathematical explanation
    limits of explanation
    mathematical proof
    proof-core
    intuitionism
    constructivsim
    Gödel’s Incompleteness Theorems
    intuitionistics mathematics
    classical mathematics
    Axiom of Choice
    Opis:
    An interview with Charles McCarty by Piotr Urbańczyk concerning  mathematical explanation.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2016, 60; 119-137
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Does Science Progress Towards Ever Higher Solvability Through Feedbacks Between Insights and Routines?
    Autorzy:
    Marciszewski, Witold
    Powiązania:
    https://bibliotekanauki.pl/articles/561316.pdf
    Data publikacji:
    2018
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    Algorithm
    arithmetic
    axiom
    axiomatic formalized theory
    concept
    decidability
    feedback
    insight (intuition)
    mathematics
    mechanism
    mentalism
    oracle
    problem
    problem-solving
    progress
    routine procedure
    science
    solvability
    Opis:
    The affirmative answer to the title question is justified in two ways: logical and empirical. (1) The logical justification is due to Gödel’s discovery (1931) that in any axiomatic formalized theory, having at least the expressive power of PA (Peano Arithmetic), at any stage of development there must appear unsolvable problems. However, some of them become solvable in a further development of the theory in question, owing to subsequent investigations. These lead to new concepts, expressed with additional axioms or rules. Owing to the so-amplified axiomatic basis, new routine procedures like algorithms, can be reached. Those, in turn, help to gain new insights which lead to still more powerful axioms, and consequently again to ampler algorithmic resources. Thus scientific progress proceeds to an ever higher scope of solvability. (2) The existence of such feedback cycles – in a formal way rendered with Turing’s systems of logic based on ordinal (1939) – gets empirically supported by the history of mathematics and other exact sciences. An instructive instance of such a process is found in the history of the number zero. Without that insight due to some ancient Hindu mathematicians there could not arise such an axiomatic theory as PA. It defines the algorithms of arithmetical operations, which in turn help intuitions; those, in turn, give rise to algorithmic routines, not available in any of the previous phases of the process in question. While the logical substantiation of the point of this essay is a well-established result of logico-semantic inquiries, its empirical claim, based on historical evidences, remains open for discussion. Hence the author’s intention to address philosophers and historians of science, and to encourage their critical responses.
    Źródło:
    Studia Semiotyczne; 2018, 32, 2; 153-185
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Almost disjoint families and property (a)
    Autorzy:
    Szeptycki, Paul
    Vaughan, Jerry
    Powiązania:
    https://bibliotekanauki.pl/articles/1205285.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    property (a), density
    extent
    almost disjoint families
    Ψ-space
    CH
    GCH
    Martin's Axiom
    $\got p = \got c$
    Cohen forcing
    Q-set
    weakly inaccessible cardinal.
    Opis:
    We consider the question: when does a Ψ-space satisfy property (a)? We show that if $|A| < \got p$ then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality $\got p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).
    Źródło:
    Fundamenta Mathematicae; 1998, 158, 3; 229-240
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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