axiom of choice
Étymologie
[modifier le wikicode]- (Date à préciser) Calque de l'allemand Axiom der Auswahl, apparu de l'article Untersuchungen über die Grundlagen der Mengenlehre I de Ernst Zermelo publié en 1908[1].
Locution nominale
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| axiom of choice \Prononciation ?\ |
axioms of choice \Prononciation ?\ |
axiom of choice \Prononciation ?\
- (Mathématiques) Axiome du choix.
If V = L then the axioms of choice and the continuum hypothesis are both true, and the assertion that a measurable cardinal exists is false.
— (Thomas Tymoczko, New Directions in the Philosophy of Mathematics: An Anthology, 1993)To clarify these ideas for the reader, let us show, without the axiom of choice, that a product of finitely many nonempty sets is nonempty: This is done by induction on the number n of sets. […] 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.
— (Bruno Poizat, traduit par Moses Klein, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, 2000)
Synonymes
[modifier le wikicode]Dérivés
[modifier le wikicode]Voir aussi
[modifier le wikicode]- axiom of choice sur l’encyclopédie Wikipédia (en anglais)
- ZFC
- Zermelo–Fraenkel set theory sur l’encyclopédie Wikipédia (en anglais)
