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Axiom

Definition

An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.

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Gödel's incompleteness theorems Gödel's second incompleteness theorem Gödel numbering Halting problem Henri Poincaré Hereditary set Hidden-variable theory Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Homology theory Homotopy theory Hyperbolic geometry Hypothesis Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Inference Infinite-valued logic Infinite set Information theory Inhabited set Injective function Integer Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Isomorphism John Cook Wilson John Stewart Bell Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Kurt Gödel Lambda calculus Large cardinal Lemma (mathematics)Lindström's theorem Line-line intersection Line segment Linear space List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and 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