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Results tagged with axiom-of-choice
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user 151152
An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.
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votes
Pathological behavior of Borel sets?
Determinacy implies that for any subset S of any Polish space and any compact K, if S contains an uncountable collection of pairwise disjoint copies of K then it contains a copy of (2^omega X K). Thi …
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