Phrase guide

axiom of countable choice

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences, set-theory

Examples

  • 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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Across languages

Translations

2 source translations are retained for this English entry.

  • Finnish: numeroituva valinta-aksiooma — axiom of set theory
  • Polish: aksjomat policzalnego wyboru — axiom of set theory