Sets And Logic 1-24
24 entries in the Sets And Logic compendium.
Set (mathematics)A set is a collection of distinct mathematical objects.Set theoryBranch of logic studying sets and mathematical foundations.Union (set theory)Set operation combining all elements from given sets.SubsetA set whose elements all belong to another set.Zermelo–Fraenkel set theoryStandard axiomatic foundation of mathematics, avoiding Russell's paradox.Sheffer strokeA logical operator equivalent to not both, also called NAND.Signature (logic)Formal description of non-logical symbols in a language.Structure (mathematical logic)A set with operations and relations used in logic.Tarski's axiomsA first-order axiom system for Euclidean geometry, complete and decidable.Tautology (logic)A formula true under all interpretations of its terms.Theory (mathematical logic)A set of sentences in a formal language.Type (model theory)A set of formulas describing possible element behavior in a structure.Type theoryFormal system classifying expressions by types to avoid paradoxes.UltraproductQuotient of a direct product modulo an ultrafilter.Universal quantificationLogical constant asserting a predicate holds for all members of a domain.Universe (mathematics)A collection containing all entities considered in a given mathematical situation.Well-formed formulaA syntactic object defined by formal grammar rules.Von Neumann universeClass of hereditary well-founded sets in ZFC set theory.Zorn's lemmaA set theory lemma equivalent to the axiom of choice.Transfinite inductionExtension of mathematical induction to ordinal numbers.Transfinite numberNumbers larger than all finite numbers, coined by Cantor in 1895.Well-ordering theoremEvery set can be well-ordered, equivalent to axiom of choice.Skolem's paradoxA countable model can contain an uncountable set.Skolem normal formA prenex normal form with only universal quantifiers.
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