An equivalent of the axiom of choice in finite models of the powerset axiom (Q752712)
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scientific article; zbMATH DE number 4179370
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An equivalent of the axiom of choice in finite models of the powerset axiom |
scientific article; zbMATH DE number 4179370 |
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An equivalent of the axiom of choice in finite models of the powerset axiom (English)
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1990
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The authors investigate finite models of the fragmentary set theory Extensionality \(+\) Powerset Axiom. In such models there is no empty set and the axiom of choice looses its meaning in view of the main result of this paper: A family of sets S has a choice set, iff its intersection \(\cap S\) exists, in which case the singleton set \(\cap S\) is the unique choice set of S.
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finite models of set theory
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Extensionality
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Powerset Axiom
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axiom of choice
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choice set
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