9 problems

Model-companion conjecture. The theory $\operatorname{GVF}_e$ has a model companion for every Archimedean error $e\geq 0$.

In a simple theory, failure of 4-amalgamation is the property under discussion. Goodrick's conjecture. Failure of 4-amalgamation comes from some, in a suitable sense, interpretable…

Let $T$ be a continuous theory. For a formula $\phi(x,y)$ and a model $M$, let $V_{\phi,M}$ be the Banach space of linear $\tilde{\phi}$-definable relations on $M$, namely the clos…

In continuous first-order logic, a theory may have the order property without having the independence property or the strict order property. Continuous-logic counterexample conject…

Let $\mathcal{T}$ be the class of $\aleph_0$-categorical, $\aleph_0$-stable classical theories in countable languages, and let $\mathcal{D}\subseteq\mathcal{T}$ consist of those th…

Let $Q$ be an $\aleph_0$-categorical, $\aleph_0$-stable theory in a countable language, and let $Q_P$ denote the theory of beautiful pairs of models of $Q$. Approximate categoricit…

Logical analyzability conjecture. The classes non-${\bf OB}$, non-${\bf FH}$ and non-${\bf F}\mathbb{R}$ are logically analyzable.

Zilber's theorem for continuous logic. Whenever $T$ is an $\aleph_0$-categorical $\aleph_0$-stable theory (in a countable language), $T_P$ is $\aleph_0$-categorical up to arbitrari…

Zilber's theorem for continuous logic, naïve version. Every $\aleph_0$-categorical $\aleph_0$-stable theory is SFB.