Set Theory & Logic
19 entries in the Set Theory & Logic compendium.
Naive set theoryInformal set theory foundational to modern mathematics.Natural transformationA morphism of functors preserving categorical structure.NegationLogical operation that inverts the truth value of a proposition.New FoundationsA non-well-founded set theory conceived by Quine.Operation (mathematics)A function combining elements of a set into another element.Ordered pairOrdered pair: a fundamental mathematical object with order significance.Partition of a setGrouping elements into non-empty, disjoint subsets that cover the whole set.Power setThe set of all subsets of a given set.Principle of explosionFrom a contradiction, any proposition can be inferred.Proof theoryProofs as formal objects analyzed by mathematical techniques.Propositional logicBranch of classical logic dealing with propositions and logical connectives.Quantifier (logic)Operators specifying how many individuals satisfy a property.Quantifier eliminationQuantifier elimination is a concept of simplification used in mathematical logic, model theory, and…RecursionA process defined by reference to a simpler version of itself.Reductio ad absurdumProof by contradiction: one of a mathematician's finest weapons.Reflexive relationA binary relation where every element relates to itself.Rice's theoremAll non-trivial semantic properties of programs are undecidable.Rule of inferenceNorms for deriving conclusions from premises in deductive logic.Russell's paradoxA set-theoretic paradox showing that unrestricted comprehension leads to contradictions.
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