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Foundations Of Mathematics

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6 domain-specific abstractions whose origin domain is Foundations Of Mathematics.

  • Index set — A set whose elements label the members of an indexed family through a declared assignment.
  • Scott–Potter set theory — Build set theory from a cumulative hierarchy of levels and histories, treating sets as subcollections of levels while allowing urelements and avoiding a primitive iterative-stage ontology.
  • Universe (mathematics) — A contextually fixed collection large enough to contain every object and construction under consideration while controlling size, paradox, and quantification in mathematical foundations.
  • Vicious circle principle — A predicativist restriction forbidding definition of an entity by quantification over a totality that already contains the entity being defined.
  • Von Neumann–Bernays–Gödel set theory — A finitely axiomatizable two-sorted set theory with sets and classes that conservatively extends ZFC for statements about sets.
  • Zermelo set theory — The original axiomatic set theory built from extensionality, elementary sets, separation, power set, union, choice, and infinity without the later replacement axiom.