Semianalytic

$X\subseteq\Bbb{R}^n$ is semianalytic if, for all $x\in\Bbb{R}^n$, there is an open neighborhood $U$ of $x$ such that $X\cap U$ is a finite Boolean combination of sets $\{\bar x\in U:f(\bar x)=0\}$ and $\{\bar x\in U:g(\bar x)>0\}$, where $f,g:U\to\Bbb{R}$ are Analytic.

See also Analytic Function, Pseudoanalytic Function, Subanalytic

References

Marker, D. ``Model Theory and Exponentiation.'' Not. Amer. Math. Soc. 43, 753-759, 1996.