Set Theory And Foundations 1-20
20 entries in the Set Theory And Foundations compendium.
Aleph numberAleph numbers measure sizes of infinite sets.AxiomA foundational statement accepted as true without proof.Axiom of choiceAxiom asserting existence of a choice function for any collection of nonempty sets.Axiom of extensionalityAxiom defining set equality by identical members.Axiom of infinityAxiom guaranteeing existence of an infinite set.Axiom of pairingAny two objects have a pair.Axiom of power setAxiom ensuring every set has a power set.Axiom of regularityAxiom ensuring no set contains itself and no infinite descending chains.Axiom of unionAxiom asserting the union of a set of sets is a set.Axiom schema of replacementAxiom schema ensuring definable images of sets are sets.Axiom schema of specificationAn axiom schema asserting any definable subclass of a set is a set.Axiomatic systemA deductive logical structure based on axioms.Cardinal numberA number measuring the size of a set.CardinalityFundamental concept defining the size of sets.Cardinality of the continuumThe cardinality of the set of real numbers.Cantor's diagonal argumentProof that some infinities are larger than others.Cantor's theoremCantor's theorem shows no set is as large as its power set.Cantor setA self-similar set with unintuitive topological properties.Class (set theory)A collection of objects defined by a property, often to avoid set-theoretic paradoxes.Complement (set theory)Set of elements not in a given set.
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