5 problems

Let $d4ae_n(N)$ denote the modified construction obtained from a tracial von Neumann algebra $N$ by gluing handles of sequentially commuting $n$ paths of Haars on pairs of independ…

Farah's conjecture. Tracial von Neumann algebras with a nontrivial type $\mathrm{II}_1$ summand are never model complete.

Model-completeness conjecture. The theory $T$ is model complete if and only if $N$ is of type I.

Quantifier-elimination conjecture. The following are equivalent:

Discrete-time approximation conjecture.