16 problems

Assume that $T$ is NIP. Let $M\prec^{+}N$, let $a\in\mathcal U$ be such that $\operatorname{tp}(a/N)$ is $M$-invariant, and let $\phi(x;y)\in L(M)$. Invariant-type quotient conject…

Let $K$ be a field considered in the ring language. A theory is n-dependent when it has no independence pattern of order $n$; 1-dependent is the corresponding usual NIP condition.…

Assume $2\leq k\in\omega$, let $T$ be a $k$-distal NIP theory, and let $G$ be a definable group. Let $\mu\in\mathfrak{M}_{G}(\mathbb{M})$ be a generically stable, $G$-invariant mea…

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 $T$ be an NIP theory, let $G$ be a definably amenable group, and let $F_M$ denote the retraction from invariant types to finitely satisfiable types, with the associated analysi…

NIP Hausdorffness conjecture. If $M$ has NIP, then $u\mathcal{M}$ is Hausdorff.

Let $H$ be a group definable in an $o$-minimal structure or a $p$-adically closed field, and assume that $H$ is a $\mathrm{dfg}$ group. Say that $H$ is bad when it has the badness…

Let $G$ be a definable, definably amenable group defined over either an $o$-minimal structure or a $p$-adically closed field. Say that $G$ is stationary when it has the stationarit…

Let $G$ be a group definable in a NIP structure. Say that $G$ is dfg if it has a definable global f-generic type, and call a global f-generic type almost periodic when its orbit un…

Let $T$ be an $NIP$ theory, let $M$ be a model of $T$, and let $G$ be a definably amenable group definable in $M$. Write $S_G(M)$ for the space of types over $M$ concentrating on…

Unstable NIP conjecture. If $T$ is an unstable NIP theory, then $T$ interprets an infinite linear order.

Assume that $M$ is a countable, saturated model of a small, NIP theory in a countable language, and let $\Delta$ be a finite set of formulas without parameters. A Polish structure…

Let $M\prec N$ be NIP $L$-structures. Let $\varphi(x,y)$ be an $L_M$-formula and let $b\in N^{|y|}$. Assume $\varphi(x,b)$ does not divide over $M$. Chernikov–Simon conjecture. The…

Let $p(x)$ be a global $M$-invariant type and let $\Delta$ be a finite set of formulas. Finite determination conjecture. There is a finite set $\Delta'$ of formulas such that, for…

Let $T$ be an NIP theory and let $M\models T$. Let $\phi(x;d)\in L(\mathcal U)$ be a formula that is non-forking over $M$. Definable $(p,q)$-conjecture. There is…

Assume that the formula $\phi(x;y)$ is NIP. Let $M$ be a model and let $\phi(x;b)\in L(\mathcal U)$ be non-dividing over $M$. Definable $(p,q)$-conjecture. There is a formula…