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Axiomatic system

Definition

In mathematics and logic, an axiomatic system or axiom system is a standard type of deductive logical structure, used also in theoretical computer science. It consists of a set of formal statements known as axioms that are used for the logical deduction of other statements. In mathematics these logical consequences of the axioms may be known as lemmas or theorems. A mathematical theory is an expression used to refer to an axiomatic system and all its derived theorems.

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Mathematical object Mathematical physics Mathematical proof Mathematical research Mathematical structure Mathematics Mathematische Grundlagen der Quantenmechanik Maurice Fréchet Measure space Measure theory Medieval Latin Metalanguage Metatheoretic Minimal axioms for Boolean algebra Model complete theory Model theory Moderne Algebra Modular lattice Monadic predicate calculus Monadic second-order logic Moritz Pasch Morphism Morse–Kelley set theory NP (complexity)Naive set theory Natural deduction Natural language Natural numbers Negation Neighbourhood (mathematics)New Foundations Nikolai Lobachevsky Noetherian ring Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Norbert Schappacher Norbert Wiener Norman Steenrod Noun Number theory Open cover Open formula Operation (mathematics)Operational calculus Order theory Ordered field Ordinal analysis Ordinal number Oscar Lanford Oscar Zariski Oswald Veblen P-adic numbers P (complexity)P versus NP problem Paradoxes of set theory Parallel axiom Parse tree Partial order Partition of a set Pasch's axiom Paul Dirac Peano axioms Permutation group Philosophy of mathematics Place (mathematics)Placeholder word Plane geometry Postulate Power set Predicate (mathematical logic)Predicate calculus Predicate logic Predicate variable Prime ideal Prime model Primitive notion Primitive recursive arithmetic Primitive recursive function Princeton Principia Mathematica Principia philosophiae cartesianae Principle of explosion Probability axioms Probability interpretations Projective algebraic variety Proof assistant Proof of impossibility Proof theory Proposition Propositional calculus Propositional formula Propositional variable Pure mathematics Quantifier (logic)Quantifier rank Quantum field theory Quantum mechanics Quasi-compact Quaternions Ramified theory of types Rational function Real analysis Real line Real number line Real vector space Recursion Recursive set Relation (mathematics)Reverse 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