14 problems

Braunfeld's monadic NIP orbit-growth conjecture. For a countable $c9$-categorical structure $c4$, $c4$ is monadically NIP if and only if

Let $M$ be a model of an NIP theory, let $G$ be a $0$-definable group in $M$, and let $N\succ M$ be an $|M|^{+}$-saturated elementary extension. Let $S_G^{\operatorname{fs}}(N,M)$…

Let $K$ be a field whose pure field theory is NIP$_n$, and let $v$ be a henselian valuation on $K$. Write $(K,v)$ for the resulting valued field. Jahnke's NIP$_n$ henselian expansi…

Let $n\geqslant 2$. A pure field is a field considered only in the language of rings, and a theory is strictly NIP$_n$ when it is NIP$_n$ but has IP$_{n-1}$. The NIP$_n$ Fields Con…

Let $G$ be a definably amenable NIP group. An fsg group is a group with finitely satisfiable generics, and a dfg group is a group with definable f-generics. Pillay–Yao's conjecture…

Let $q\geq 2$ be an integer, $M$ be an $L$-structure, and let $\varphi(x,y)$ be an $L(M)$-formula with dual shatter function $\pi_{\varphi}^*(n)\in o(n^q)$. A family of instances…

Pure-field NIP$_n$ conjecture. For every $n\geqslant 2$, no strictly NIP$_n$ pure fields exist; equivalently, a pure field is NIP$_n$ if and only if it is NIP.

Classification conjecture. Any strongly NIP ordered field $(K,<)$ is almost real closed.

Let $(R,<,+)$ be a dense archimedean ordered abelian group, let ${\mathscr{R}}$ be a strongly dependent and noiseless expansion, and let ${\mathscr{N}}$ be a highly saturated eleme…

Let $(R,<,+)$ be a dense archimedean ordered abelian group, let ${\mathscr{R}}$ be an expansion of it, and let ${\mathscr{R}}^{\square}$ be the completion structure used in the pap…

Let $M$ be a finitely homogeneous NIP structure. Structural conjecture. The following hold: 1. The automorphism group $\operatorname{Aut}(M)$ acts oligomorphically on the space of…

A field is NIP if its theory has the non-independence property. The superrosy NIP field conjecture. Every infinite superrosy field with NIP is either algebraically closed or real c…

Algebraic-or-real-closed field conjecture. The field $K$ is either algebraically closed or real closed.

Solvable-by-finite conjecture. Then $G$ is solvable-by-finite.