  Suppose that $\Omega$ is a complex lattice that is closed under complex
conjugation and that $I$ is a small real interval, and that $D$ is a disc in $
\mathbb{C}$. Then the restriction $\wp|_D$ is definable in the structure
$(\bar{\mathbb{R}},\wp|_I)$ if and only if the lattice $\Omega$ has complex
multiplication. This characterises lattices with complex multiplication in
terms of definability.

Logic