Results 291 to 300 of about 107,162 (337)
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The shrinking principle and the axiom of choice
Monatshefte für Mathematik, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Banaschewski B, Schuster, Peter Michael
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1974
For the deepest results about partially ordered sets we need a new settheoretic tool; we interrupt the development of the theory of order long enough to pick up that tool.
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For the deepest results about partially ordered sets we need a new settheoretic tool; we interrupt the development of the theory of order long enough to pick up that tool.
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2012
In 1904, Zermelo published his first proof that every set can be well-ordered. The proof is based on the so-called Axiom of Choice, denoted AC, which, in Zermelo’s words, states that the product of an infinite totality of sets, each containing at least one element, itself differs from zero (i.e., the empty set).
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In 1904, Zermelo published his first proof that every set can be well-ordered. The proof is based on the so-called Axiom of Choice, denoted AC, which, in Zermelo’s words, states that the product of an infinite totality of sets, each containing at least one element, itself differs from zero (i.e., the empty set).
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2002
The Axiom of Choice was first enunciated by Zermelo. The standard formulation is as follows.
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The Axiom of Choice was first enunciated by Zermelo. The standard formulation is as follows.
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Determinate logic and the Axiom of Choice
Annals of Pure and Applied Logic, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Independence of a Strong Axiom of Choice
The Mathematical Gazette, 1962There is a growing realization among mathematicians and logicians of the many-sided role played by the axiom of choice in various branches of mathematics. Many of them tend to accept the axiom of choice as a legitimate principle provided, of course, it is proved to be independent in a suitable axiom system. This tendency has been accelerated by Gödel’s
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On Martin's Axiom and Forms of Choice
Mathematical Logic Quarterly, 2016Martin's Axiom is the statement that for every well‐ordered cardinal , the statement holds, where is “if is a c.c.c. quasi order and is a family of dense sets in P, then there is a ‐generic filter of P”. In , the fragment is provable, but not in general in .
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The Concept of State and the Axiom of Choice
Journal of the Franklin Institute, 1977Abstract The first part of the paper is concerned with the problem of existence of state space representations of general systems. It is shown that the axiom of choice makes possible the direct construction of a reduced state space representation of a general system under no restrictive hypotheses.
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1991
AbstractIn § 9.4 a principle — the axiom of countable choice — was introduced which differed from the axioms of this book's default theory because it asserted the existence of a set of a particular sort (actually, in this case, a sequence) without supplying a condition that characterizes it uniquely.
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AbstractIn § 9.4 a principle — the axiom of countable choice — was introduced which differed from the axioms of this book's default theory because it asserted the existence of a set of a particular sort (actually, in this case, a sequence) without supplying a condition that characterizes it uniquely.
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Cancer epigenetics in clinical practice
Ca-A Cancer Journal for Clinicians, 2023Veronica Davalos, Manel Esteller
exaly