Decidability of the real exponential field (Rexp)

Determine the decidability of the first-order theory of the real field expanded by the total exponential function, specifically the theory of the o-minimal structure Rexp = (R; <, +, ·, exp).

Background

Tarski's Problem asks for extending semialgebraic geometry to include the real exponential function. Wilkie's theorem establishes that Rexp is o-minimal, providing a geometric resolution, but the logical decidability of its first-order theory remains unresolved and is linked to the real Schanuel's Conjecture.

This question is central to understanding the algorithmic properties of definable sets and functions involving exp and has implications for the foundations of tame geometry used in optimization and deep learning.