5 problems

Let $n$ be a finite dimension, and let ${\sf VT}(l,m)$ denote that Vaught's theorem holds at parameters $l$ and $m$, where $n\leq l,m\leq\omega$. For $n\leq l<m\leq\omega$, this me…

Tarski's atomlessness conjecture. When $\alpha$ is infinite, $\mathfrak{Fr}_m\mathrm{CA}_{\alpha}$ has no atoms other than its $2^m$ zero-dimensional atoms; equivalently, after acc…

Tarski's atom conjecture. All atoms in $\mathfrak{Fr}_m\mathrm{CA}_{\alpha}$ are zero-dimensional.

Strong representability conjecture for $\alpha({\bf G})$. The relation-algebra atom structure $\alpha({\bf G})$ is strongly representable if and only if ${\mathfrak{M}}({\bf G})$ i…

Let a monadic De Morgan reduct be the reduct of a suited IFG$_1$-algebra to the signature … Let $\mathcal K^{\nabla_1}$ be the variety defined in the surrounding algebraic framewor…