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About: Tarski's axiomatization of the reals     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatMathematicalAxiomsyago:WikicatOrderedGroupsyago:Abstraction100002137yago:AuditoryCommunication107109019yago:Communication100033020yago:ComplexNumber113729428yago:DefiniteQuantity113576101yago:Group100031264yago:Maxim107152948yago:Measure100033615yago:Number113582013yago:RealNumber113729902yago:Saying107151380yago:Speech107109196yago:WikicatRealNumbers New Facet based on Instances of this Class

In 1936, Alfred Tarski set out an axiomatization of the real numbers and their arithmetic, consisting of only the 8 axioms shown below and a mere four primitive notions: the set of reals denoted R, a binary total order over R, denoted by infix <, a binary operation of addition over R, denoted by infix +, and the constant 1. The term "Tarski's axiomatization of real numbers" also refers to the theory of real closed fields, which Tarski showed completely axiomatizes the first-order theory of the structure 〈R, +, ·, <〉.