Results 221 to 230 of about 4,367 (259)
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Łoś's theorem and the axiom of choice
Mathematical Logic Quarterly, 2019AbstractIn set theory without the Axiom of Choice (), we investigate the problem of the placement of Łoś's Theorem () in the hierarchy of weak choice principles, and answer several open questions from the book Consequences of the Axiom of Choice by Howard and Rubin, as well as an open question by Brunner. We prove a number of results summarised in § 3.
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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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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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2013
The ZF axioms allow us to assert the existence of any set whose members are selected according to some definable “rule”—this is essentially what the replacement schema says. However, we often want to assert the existence of a set without knowing a rule for selecting its members.
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The ZF axioms allow us to assert the existence of any set whose members are selected according to some definable “rule”—this is essentially what the replacement schema says. However, we often want to assert the existence of a set without knowing a rule for selecting its members.
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Paracompactness of Metric Spaces and the Axiom of Multiple Choice
Mathematical Logic Quarterly, 2000Kyriakos Keremedis, Jean E Rubin
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Disasters in topology without the axiom of choice
Archive for Mathematical Logic, 2001Kyriakos Keremedis, Keremedis Kyriakos
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Metric spaces and the axiom of choice
Mathematical Logic Quarterly, 2003Omar De La Cruz +2 more
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Sequential topological conditions in ℝ in the absence of the axiom of choice
Mathematical Logic Quarterly, 2003Gonçalo Gutierres
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Some Weak Forms of the Axiom of Choice Restricted to the Real Line
Mathematical Logic Quarterly, 2001Kyriakos Keremedis +1 more
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