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axiom of empty set : ウィキペディア英語版
axiom of empty set

In axiomatic set theory, the axiom of empty set is an axiom of Kripke–Platek set theory and the variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo set theory and Zermelo–Fraenkel set theory, with or without the axiom of choice.
== Formal statement ==
In the formal language of the Zermelo–Fraenkel axioms, the axiom reads:
:\exists x\, \forall y\, \lnot (y \in x)
or in words:
:There is a set such that no set is a member of it.

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