Example image of eyePlorer eyePlorer map for 'Axiom of regularity': Zermelo–Fraenkel set theory First-order logic Sequence Set (mathematics) Axiom of choice Ordinal Well-order Non-well-founded set theory Epsilon-induction Axiom of pairing Axiom schema of replacement Function (mathematics) Natural number Axiom of infinity Hereditarily finite set Ultraproduct Model theory Ordered pair Kazimierz Kuratowski Naive set theory Russell's paradox Consistency Axiom schema of specification Subset Class (set theory) Von Neumann universe Scott's trick Well-founded relation Constructive set theory General Formal Ontology Kripke–Platek set theory with urelements Well-ordering principle Ackermann set theory Tarski–Grothendieck set theory Mostowski collapse lemma Category of sets Kripke–Platek set theory Quasi-set theory Morse–Kelley set theory Axiom of extensionality Zermelo set theory Regular Constructible universe Infinitary logic John von Neumann Hypergraph Universe (mathematics) Ordinal number Scott–Potter set theory Mereology