## Cells

Let $\M$ be an o-minimal expansion of a dense linear order $(M,\lt)$, and let $n \in \NN$ be nonzero. Inspired by this post, we now make the following Definition Let $\sigma \in \{0,1\}^n$ and set $\sigma’:= \sigma \rest{\{0,1\}^{n-1}}$. We say that a definable set $C \subseteq M^n$ is a $\sigma$-cell whenever the following holds: if…