| Title:
|
Linear extenders and the Axiom of Choice (English) |
| Author:
|
Morillon, Marianne |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
419-434 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In set theory without the Axiom of Choice ZF, we prove that for every commutative field $\mathbb K$, the following statement $\mathbf D_{\mathbb K}$: ``On every non null $\mathbb K$-vector space, there exists a non null linear form'' implies the existence of a ``$\mathbb K$-linear extender'' on every vector subspace of a $\mathbb K$-vector space. This solves a question raised in Morillon M., {Linear forms and axioms of choice}, Comment. Math. Univ. Carolin. {50} (2009), no. 3, 421-431. In the second part of the paper, we generalize our results in the case of spherically complete ultrametric valued fields, and show that Ingleton's statement is equivalent to the existence of ``isometric linear extenders''. (English) |
| Keyword:
|
Axiom of Choice |
| Keyword:
|
extension of linear forms |
| Keyword:
|
non-Archimedean fields |
| Keyword:
|
Ingleton's theorem |
| MSC:
|
03E25 |
| MSC:
|
46S10 |
| idZBL:
|
Zbl 06837076 |
| idMR:
|
MR3737115 |
| DOI:
|
10.14712/1213-7243.2015.223 |
| . |
| Date available:
|
2017-12-12T06:43:08Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146987 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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