Linked from

The 37 pages that link to Axiom, each with the reason it gives.

• Set theoryRelated: Axioms specify which sets exist and which operations preserve sethood.

• Non-Euclidean geometryNarrower topic: Different choices of geometric axioms define different consistent geometries.

• Mathematical proofRelated: Axioms supply premises from which proofs derive further statements.

• Rule of inferenceCompared with: Unlike an inference rule, an axiom contributes a starting formula rather than a transition.

• Formal proofRelated: Axioms supply premises from which a derivation can begin.

• Principia MathematicaRelated: The work’s derivations proceed from explicitly stated logical axioms.

• ConsistencyRelated: Changing a theory’s axioms can change whether it has a contradiction.

• Mathematical logicRelated: Axioms supply the premises from which formal proofs derive theorems.

• SoundnessRelated: Soundness also requires the system's axioms to hold in its intended models.

• DefinitionCompared with: Definitions specify meanings; axioms assert properties of the objects so specified.

• TheoremRelated: Axioms supply premises from which theorems in a theory can be derived.

• Axiomatic methodBroader topic: Axioms supply the initial statements from which the method derives its results.

• FormalismRelated: Formal mathematical derivations begin from stipulated axioms rather than semantic truths.

• MathematicsRelated: Axioms set the premises from which mathematical theories derive results.

• LogicismRelated: A logicist derivation must distinguish logical axioms from principles that add mathematical content.

• Axiom of pairingNarrower topic: Pairing is an axiom because its existence claim is assumed in the theory.

• Nikolai LobachevskyNarrower topic: Lobachevsky’s work demonstrated the consequences of altering a foundational geometric assumption.

• DemonstrationRelated: Axioms can serve as the initial premises from which demonstrations derive results.

• Foundations of GeometryNarrower topic: Geometric foundations begin by specifying which statements about space are assumed.

• Geometric proofNarrower topic: Geometric proofs begin from accepted assumptions such as Euclid’s postulates.

• Philosophy of mathematicsRelated: The status and justification of axioms shape accounts of mathematical foundations.

• Algebraic structureRelated: Axioms specify which laws the operations of a structure must satisfy.

• Axiom schemaNarrower topic: A schema specifies many axioms, while an axiom is one statement in the resulting family.

• Axiomatic systemBroader topic: Axioms supply the premises from which the system's theorems are derived.

• Deductive systemRelated: Axioms can begin derivations without being derived within the system.

• Hilbert's axiomsNarrower topic: Each group supplies assumptions from which geometric theorems can be proved.

• János BolyaiNarrower topic: Treating geometry’s postulates as assumptions made it possible to test alternatives.

• Mathematical structureRelated: Axioms constrain which interpretations count as structures of a given kind.

• Abstract data typeRelated: Axioms can express operation laws, such as how insertion and removal interact.

• Mathematical conjectureCompared with: Unlike a conjecture, an axiom is adopted as a starting assumption.

• Formal scienceBroader topic: Axioms provide premises from which formal theories derive further statements.

• Tarski's axiomsRelated: Each axiom constrains the point relations from which geometric theorems are derived.

• Playfair's axiomNarrower topic: Playfair's statement is adopted as a basic assumption in Euclidean geometry.

• Axiom of Empty SetNarrower topic: The axiom of empty set is one assumption in an axiomatic theory.

• Axiom of limitation of sizeNarrower topic: Limitation of size is an axiom schema or principle within class theories.

• Base (foundation)Related: Axioms form the foundational premises from which formal results are derived.

• Mathematical conceptsRelated: Axioms determine the rules from which mathematical results are derived.