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axiom of countable choiceとは 意味・読み方・使い方
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意味・対訳 可算選択公理(英: Axiom of countable choice)とは、公理的集合論における公理のひとつで、空でない集合からなる可算な集合族があったときに、それぞれの集合から一つずつ元を選び出して新しい集合を作ることができるという公理である。
Wiktionary英語版での「axiom of countable choice」の意味 |
axiom of countable choice
名詞
- (set theory) A weaker form of the axiom of choice that states that every countable collection of nonempty sets must have a choice function; equivalently, the statement that the direct product of a countable collection of nonempty sets is nonempty.
- 2000, Moses Klein (translator), Bruno Poizat, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, Springer, page 169,
- The finite axiom of choice is not an axiom, but rather a theorem that can be proved from the other axioms. In contrast, there are weak forms of the axiom of choice that are not provable. One example is the axiom of countable choice, which states that if form a denumerable set of nonempty sets, their product is nonempty. […] The axiom of countable choice is constantly used in analysis; it is often hidden so as not to sow confusion in the minds of the students (who are inclined to accept anything desired) or of the professors (who do not like to shake the foundations of the discipline).
- 2012, Richard G. Heck, Jr., Reading Frege's Grundgesetze, Oxford University Press, page 271,
- But, once again, while we can easily prove
- we have no way to infer
- without an axiom of countable choice.
- But, once again, while we can easily prove
- 2013, Valentin Blot, Colin Riba, On Bar Recursion and Choice in a Classical Setting, Chung-chien Shan (editor), Programming Languages and Systems: 11th International Symposium, APLAS 2013, Proceedings, Springer, LNCS 8301, page 349,
- We show how Modified Bar-Recursion, a variant of Spector's Bar-Recursion due to Berger and Oliva can be used to realize the Axiom of Countable Choice in Parigot's Lambda-Mu-calculus, a direct-style language for the representation and evaluation of classical proofs.
- 2000, Moses Klein (translator), Bruno Poizat, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, Springer, page 169,
同意語
Further reading
- Axiom of choice on Wikipedia.
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