In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form

In 1936, Alfred Tarski gave an axiomatization of the real numbers and their arithmetic, consisting of only the eight axioms shown below and a mere four primitive notions: the set of reals denoted R, a binary relation over R, denoted by infix <, a binary operation of addition over R, denoted by infix +, and the constant 1.

(slang) For real.