3 problems

Let $M$ be a highly saturated $P$-minimal structure over a $p$-adic field $K$, let $G$ be a definable group, and set $n=\dim(G)$. Let $M_0\prec M$ be a small model defining $G$. Re…

Let $M$ be a highly saturated $P$-minimal structure over a $p$-adic field $K$, and let $G$ be an $n$-dimensional definable group. Recall that $G^{00}$ is the smallest type-definabl…

Let $K$ be a $p$-adically closed field, let $(K,\mathcal{L})$ be a $P$-minimal structure, and let $X\subseteq K$. A function $f:X\to K$ is locally strictly monotone on a set…