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Results tagged with axiom-of-choice
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user 6401
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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Nilradicals without Zorn's lemma
Y. Rav proved this using the Ultrafilter Principle ("Every filter on a set can be extended to an ultrafilter"), which is weaker than the Axiom of Choice. Theorem 4.1 of Variants of Rado's selection le …
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