An intuitionistic version of Zermelo's proof that every choice set can be well-ordered (Q2758049)
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scientific article; zbMATH DE number 1679322
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An intuitionistic version of Zermelo's proof that every choice set can be well-ordered |
scientific article; zbMATH DE number 1679322 |
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An intuitionistic version of Zermelo's proof that every choice set can be well-ordered (English)
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5 July 2002
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axiom of choice
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well-ordering
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intuitionistic set theory
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elementary topos
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choice function
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0.88682485
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0.88535225
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0.8764622
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0.86249995
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0.86229014
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The well-known theorem of Zermelo states that any set possessing a choice function for its set of non-empty subsets can be well-ordered. The paper under review presents a generalization of Zermelo's own proof of the theorem that is valid in any elementary topos. It is, however, doubtful that the proof may be called ``intuitionistic'', because the form of the generalized inductive definition it uses is not likely to be acceptable intuitionistically.
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