About: Tarski's axioms

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Tarski's axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry that is formulable in first-order logic with identity, and requiring no set theory (i.e., that part of Euclidean geometry that is formulable as an elementary theory). Other modern axiomizations of Euclidean geometry are Hilbert's axioms and Birkhoff's axioms.

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  • Les axiomes de Tarski, dus à Alfred Tarski, sont un système d'axiomes pour la géométrie euclidienne exprimé en logique du premier ordre. Les prédicats utilisés dans le langage sont : * le point y est entre les points x et z : (entre deux ou en anglais betweenness) ; * la distance de x à y est égale à la distance de z à u : (congruence). (fr)
  • Tarski's axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry that is formulable in first-order logic with identity, and requiring no set theory (i.e., that part of Euclidean geometry that is formulable as an elementary theory). Other modern axiomizations of Euclidean geometry are Hilbert's axioms and Birkhoff's axioms. (en)
  • Аксиоматика Тарского — система аксиом элементарной евклидовой геометрии, предложенная Альфредом Тарским.Замечательна тем, что формулируется в логике первого порядка с равенством и не требует теории множеств. (ru)
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  • Les axiomes de Tarski, dus à Alfred Tarski, sont un système d'axiomes pour la géométrie euclidienne exprimé en logique du premier ordre. Les prédicats utilisés dans le langage sont : * le point y est entre les points x et z : (entre deux ou en anglais betweenness) ; * la distance de x à y est égale à la distance de z à u : (congruence). (fr)
  • Tarski's axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry that is formulable in first-order logic with identity, and requiring no set theory (i.e., that part of Euclidean geometry that is formulable as an elementary theory). Other modern axiomizations of Euclidean geometry are Hilbert's axioms and Birkhoff's axioms. (en)
  • Аксиоматика Тарского — система аксиом элементарной евклидовой геометрии, предложенная Альфредом Тарским.Замечательна тем, что формулируется в логике первого порядка с равенством и не требует теории множеств. (ru)
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  • Tarski's axioms (en)
  • Axiomes de Tarski (fr)
  • Аксиоматика Тарского (геометрия) (ru)
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