 Existential theory of the reals

The Existential Theory of the Reals, often discussed in the context of mathematical logic and model theory, relates to the study of the properties of real numbers as represented in certain logical frameworks. It focuses on the notion of whether certain mathematical statements can be expressed as true or false when considering the real numbers. In particular, the existential theory of the reals often examines the sets of real numbers defined by existentially quantified formulas. These formulas are statements that assert the existence of certain elements satisfying given conditions.