Last Updated
：2025/12/04
axiom of countable choice
Noun
Japanese Meaning
可算選択公理とは、集合論における選択公理の弱い形であり、非空集合からなる可算個の集合族に対して、各集合から一つずつ要素を選ぶ選択関数が存在すること、すなわち可算個の非空集合の直積が非空であるという主張に同値する。
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(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.
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axiom of countable choice
When teaching introductory set theory, I always emphasize the axiom of countable choice and how it differs from the full axiom of choice.
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When teaching introductory set theory, I always emphasize the axiom of countable choice and how it differs from the full axiom of choice.
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