The main result of this paper is the following: if the Weierstrass division theorem is valid in a quasianalytic differentiable system, then this system is contained in the system of analytic germs. This result has already been known for particular examples, such as the quasianalytic Denjoy-Carleman classes.

Given adjacent subanalytic strata $(X,Y)$ in ${\mathbf{R}}^n$ verifying Kuo’s ratio test $\left(r\right)$ (resp. Verdier’s $\left(w\right)$-regularity) we find an open dense subset of the codimension $k$$C^1$ submanifolds $W$ (wings) containing $Y$ such that $(X\cap W,Y)$ is generically Whitney $\left(b^{\pi }\right)$-regular is exactly one more than the dimension...

The aim of this paper is to prove that every subset of ${ℝ}^n$ definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).