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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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Compactness and the Axiom of Choice
Applied Categorical Structures, 1996Four versions of compactness (equivalent in ZFC) and their properties are investigated without the axiom of choice. All the four versions are equivalent iff the axiom of choice holds (many equivalent forms concerning mainly products of spaces are given).
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Distributivity and an axiom of choice
Journal of Symbolic Logic, 1954In this paper a theorem will be established which states that a particular axiom of choice is equivalent to complete distributivity of union and intersection. The theorem will be formulated and proved in the system of logic of [4]. In addition to definitions of [4], the following will be used.In terms of these definitions, the theorem can be formulated
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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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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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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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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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2018
The axiom of choice is a mathematical postulate about sets: for each family of non-empty sets, there exists a function selecting one member from each set in the family. If those sets have no member in common, it postulates that there is a set having exactly one element in common with each set in the family. First formulated in 1904, the axiom of choice
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The axiom of choice is a mathematical postulate about sets: for each family of non-empty sets, there exists a function selecting one member from each set in the family. If those sets have no member in common, it postulates that there is a set having exactly one element in common with each set in the family. First formulated in 1904, the axiom of choice
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