7 problems

Assume that $T$ is a first-order theory and that … with $2^\lambda=\lambda^+$. Let $\langle M_\alpha:\alpha<\lambda^+\rangle$ be a $\prec$-increasing continuous sequence with…

No strictly $n$-dependent fields conjecture. There are no strictly $n$-dependent fields for $n\geq 2$.

Fix a dependent diagram $D$ and a strongly compact cardinal $\theta>|T|$. Let $\theta<\lambda=\lambda^{<\lambda}$ and $\lambda^{+}=2^{\lambda}$. Let … be an increasing continuous s…

Let $T$ be dependent, let $|T|<\lambda=\lambda^{<\lambda}$, let $\lambda^+=2^\lambda$, and let $\sigma=\operatorname{cf}(\sigma)<\lambda$. Suppose…

Let $T$ be a first-order theory, let $M$ be a model of $T$, and let $\kappa$ be an infinite cardinal. A sequence $\langle a_\alpha:\alpha<\delta\rangle$ in $M$ is indiscernible whe…

Stability conjecture for strongly $2$-dependent groups. Every strongly $2$-dependent group is stable; equivalently, if $G$ is a group such that

Frank Wagner's conjecture. There is some $n$ such that, for every finite set $v\subseteq\omega$, the intersection