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#axiom_of_regularity

Axiom of regularity

Axiom of set theory

In mathematics, the axiom of regularity is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads:

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Axiom of regularity Zermelo–Fraenkel set theory Von Neumann universe Von Neumann–Bernays–Gödel set theory List of axioms Non-well-founded set theory Universal set Axiom of extensionality Ackermann set theory Axiom schema of specification
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