## Angular level

(Joint work with Tobias Kaiser) The goal of this post is to introduce a rough measure of size for a real domain $U$, based on the level of its boundary function $f_U$. As before, “definable” means “definable in $\Ranexp$”. Let $\I$ be the set of all infinitely increasing $\,f \in \H$ and set \$\bo:= \H_{\gt…