Linked from

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

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

• 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.

• 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.

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

• 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.

• 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.