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Results tagged with axiom-of-choice
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user 151109
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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Pathological behavior of Borel sets?
The following statement is equivalent to the perfect set property for Pi^1_1, hence not decidable in ZFC: Every sigma-compact subset of R^2 which contains uncountably many pairwise disjoint topologic …
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