axiom of choice

== Anglais == === Étymologie === (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. === Locution nominale === 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) La traduction en français de l’exemple manque. (Ajouter) 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) La traduction en français de l’exemple manque. (Ajouter) ==== Synonymes ==== AC ==== Dérivés ==== axiom of countable choice axiom of denumerable choice axiom of dependent choice === Voir aussi === axiom of choice sur l’encyclopédie Wikipédia (en anglais) ZFC Zermelo–Fraenkel set theory sur l’encyclopédie Wikipédia (en anglais) === Références ===