 Decidability of first-order theories of the real numbers

The decidability of first-order theories of the real numbers is a significant topic in mathematical logic, particularly concerning model theory and the foundations of mathematics. In general terms, a first-order theory consists of a set of axioms and rules for reasoning about a particular mathematical domain. When we talk about the first-order theory of the real numbers, we typically refer to the standard axioms that describe the real numbers, including properties of addition, multiplication, order, and the completeness property of the reals.