Maximal ideals and the axiom of choice (Q2772752)
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scientific article; zbMATH DE number 1708196
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximal ideals and the axiom of choice |
scientific article; zbMATH DE number 1708196 |
Statements
13 May 2002
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axiom of choice
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Boolean prime ideal theorem
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maximal filter
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maximal ideal
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weak choice principles
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open problems
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Maximal ideals and the axiom of choice (English)
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Working in ZF set theory without the axiom of choice, the author provides a highly useful survey of the relative positions of maximal ideal (resp. filter) theorems in the hierarchy of weak choice principles in algebra, topology, order theory, graph theory, propositional logic, complexity theory, welfare theory, and quantum logic. The author singles out and discusses seven open problems that ``serve as an illustration of how `mainstream' mathematics (in ZFC) might be stimulated by the study of weak choice principles''.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00067].
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