7 problems

Let $G=G(\mathfrak{C})$ be a definable group, and let $\mu\in\mathfrak{M}^{\operatorname{def}}_G(\mathfrak{C},M)$ be fim over $M$. Its right stabilizer, denoted…

Let $T$ be an $m$-distal theory, and let $n>m>0$. For global generically stable measures $\mu_0(x_0),\ldots,\mu_{n-1}(x_{n-1})$, write … A tuple of measures is $m$-determined when…

Let $\bar m$ enumerate a tuple from a small model $M\preceq\mathfrak{C}$, and let $\mu\in\mathfrak{M}^{\operatorname{def}}_{\bar m}(\mathfrak{C},M)$ be fim over $M$. By the cited r…

The automorphism-group idempotent fim measure conjecture. The following conditions are equivalent: (i) $\mu$ is idempotent with respect to the new convolution product; (ii) $\mu$ i…

Let $\mathcal{R}_3$ be the universal homogeneous $3$-hypergraph. An invariant Keisler measure for $\mathcal{R}_3$ is ergodic if it is an extreme point of the convex space of invari…

Let $u$ be a Keisler measure. A measure is generically stable and idempotent when it has the corresponding properties under definable convolution, and it is support transitive whe…

Let $T$ be a theory, let $\mathcal{U}$ be a monster model of $T$, and let $\mu\in\mathfrak{M}_x(\mathcal{U})$ be a Keisler measure. A measure is dfs if it is definable and finitely…