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Results tagged with axiom-of-choice
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user 21241
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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What are the known implications of "There exists a Reinhardt cardinal" in the theory "ZF + j"?
First, let's show that I-1 implies I0:
Suppose $I-1(\kappa,\delta, j)$; we may assume, by forcing if necessary, that $V_\kappa$ (and hence $V_\delta$) satisfies the Axiom of Choice. Now if j is a ran …
