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 setA partition groups elements into disjoint, non-empty subsets.Power setThe set of all subsets of a given set.Principle of explosionFrom a contradiction, any statement can be proven.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 eliminationSimplification of quantified statements to quantifier-free equivalents.RecursionA process defined by reference to a simpler version of itself.Reductio ad absurdumArgument form that proves a claim by showing its opposite leads to absurdity.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 paradox showing unrestricted set comprehension leads to contradiction.
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