3 problems

Let $M$ be a $p$-adic closed field and let $G$ be a group definable in $M$. The profinite Ellis group conjecture. The Ellis group of the flow $S_{G,\operatorname{ext}}(M)$ is abstr…

Let $M\prec^*N$ be a $*$-elementary extension, meaning that $N$ is obtained from an elementary extension of $M_{ext}$ in the language $\mathcal{L}_{ext,M}$ by reduct to the origina…

Let $M$ be a first-order structure and let $G$ be an $M$-definable group. The space $S_{ext,G}(M)$ is the universal definable flow of $G$ over $M$, and $G^{00}$ is the smallest typ…