Results 321 to 330 of about 250,783 (371)
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The Bounded Axiom A Forcing Axiom
Mathematical Logic Quarterly, 2010AbstractWe introduce the Bounded Axiom A Forcing Axiom (BAAFA). It turns out that it is equiconsistent with the existence of a regular ∑2‐correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom (BPFA) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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The Induction Axiom and the Axiom of Choice
Mathematical Logic Quarterly, 1961Verf. schlägt eine Modifikation des Peanoschen Axiomensystems für die natürlichen Zahlen vor, bei der statt des einwertigen Funktionsbegriffs, wie er bei der Nachfolgefunktion auftritt, der Begriff der mehrwertigen Funktion gebraucht wird, so daß es z. B. zu einer Zahl mehrere Nachfolger gibt. Die Peanoschen Axiome werden entsprechend verändert.
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Results in Mathematics, 2021
The paper under review is set in the context of plane absolute geometry and Hilbert planes, in the absence of any assumption on continuity that implies the Archimedean axiom. In this context, many statements that are usually considered equivalent to the Euclidean parallel postulate \textbf{P} turn out to be weaker than it.
Victor Pambuccian, Celia Schacht
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The paper under review is set in the context of plane absolute geometry and Hilbert planes, in the absence of any assumption on continuity that implies the Archimedean axiom. In this context, many statements that are usually considered equivalent to the Euclidean parallel postulate \textbf{P} turn out to be weaker than it.
Victor Pambuccian, Celia Schacht
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Efficient MUS Enumeration of Horn Formulae with Applications to Axiom Pinpointing
International Conference on Theory and Applications of Satisfiability Testing, 2015The enumeration of minimal unsatisfiable subsets (MUSes) finds a growing number of practical applications, that includes a wide range of diagnosis problems.
M. F. Arif +2 more
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The American Mathematical Monthly, 1975
hItroduction. During the past decade, many new axioms of set theory have appeared. The principal object of these axioms is to settle important problems which cannot be settled without new axioms. Thus Godel and Cohen have shown that the Continuum Hypothesis cannot be settled on the basis of the presently accepted axioms; so it is natural to look for ...
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hItroduction. During the past decade, many new axioms of set theory have appeared. The principal object of these axioms is to settle important problems which cannot be settled without new axioms. Thus Godel and Cohen have shown that the Continuum Hypothesis cannot be settled on the basis of the presently accepted axioms; so it is natural to look for ...
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The Journal of Symbolic Logic, 2015
AbstractThe resurrection axioms are forms of forcing axioms that were introduced recently by Hamkins and Johnstone, who developed on earlier ideas of Chalons and Veličković. In this note, we introduce a stronger form of resurrection (which we callunboundedresurrection) and show that it gives rise to families of axioms which are consistent relative to ...
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AbstractThe resurrection axioms are forms of forcing axioms that were introduced recently by Hamkins and Johnstone, who developed on earlier ideas of Chalons and Veličković. In this note, we introduce a stronger form of resurrection (which we callunboundedresurrection) and show that it gives rise to families of axioms which are consistent relative to ...
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The equivalence of Axiom (∗)+ and Axiom (∗)++
Journal of Mathematical LogicAsperó and Schindler have completely solved the Axiom [Formula: see text] vs. [Formula: see text] problem. They have proved that if [Formula: see text] holds then Axiom [Formula: see text] holds, with no additional assumptions. The key question now concerns the relationship between [Formula: see text] and Axiom [Formula: see text]. This is because the
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Theory of Probability & Its Applications, 1994
Summary: An axiomatic system of probability theory is outlined in which randomness and independence are taken as primitives. Such approach goes back to von Mises. The axioms proposed contradict the axiom of choice, but are compatible with the axiom of dependent choice, and this is sufficient for practical needs.
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Summary: An axiomatic system of probability theory is outlined in which randomness and independence are taken as primitives. Such approach goes back to von Mises. The axioms proposed contradict the axiom of choice, but are compatible with the axiom of dependent choice, and this is sufficient for practical needs.
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Journal of Knot Theory and Its Ramifications, 2006
We prove that the two conditions from the definition of a biquandle by Fenn, Jordan-Santana, Kauffman [1] are equivalent and thus answer a question posed in the paper. We also construct a weak biquandle, which is not a biquandle.
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We prove that the two conditions from the definition of a biquandle by Fenn, Jordan-Santana, Kauffman [1] are equivalent and thus answer a question posed in the paper. We also construct a weak biquandle, which is not a biquandle.
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Philosophia Mathematica, 1998
The author discusses various topics such as: the transition from informal concepts to mathematically precise notions (on the examples of natural numbers, continuous functions, area, distribution, recursiveness, random sequences, choice sequences (which receive most of the author's attention), infinitesimals). The paper ends with a discussion of various
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The author discusses various topics such as: the transition from informal concepts to mathematically precise notions (on the examples of natural numbers, continuous functions, area, distribution, recursiveness, random sequences, choice sequences (which receive most of the author's attention), infinitesimals). The paper ends with a discussion of various
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