KnowraAxiom of determinacyLinked fromLinked fromThe 7 pages that link to Axiom of determinacy, each with the reason it gives.All 7Related 2Compared with 5Axiom of choiceCompared with: For sets of reals, it conflicts with full choice and implies different structural consequences.Choice functionCompared with: In common set-theoretic settings it conflicts with the full axiom of choice.Descriptive set theoryRelated: It implies powerful regularity properties for sets of reals, contrary to the axiom of choice.Martin's axiomCompared with: It represents a competing foundational direction with consequences for sets of real numbers unlike Martin's axiom.Nonmeasurable setRelated: Under determinacy assumptions, broad classes of sets of reals have regularity properties that rule out familiar pathologies.Large cardinalCompared with: It conflicts with the axiom of choice but shares deep consistency-strength connections with large cardinals.Hausdorff paradoxCompared with: Set theories replacing the full axiom of choice can rule out some pathological decompositions.