4 problems

Let $\scalebox{1.15}{\textsf{\upshape A}}^{\left(n\right)}$ and $\scalebox{1.15}{\textsf{\upshape C}}^{\left(n'\right)}$ be a polyadic associative algebra and a coassociative coalg…

Rainbow indistinguishability conjecture. The two algebras cannot be distinguished by any $n$-variable diagonal-free equation.

Let $\alpha$ be an infinite dimension and let $\kappa\leq |\alpha|$. Consider the classical polyadic algebra $\mathsf{PA}_{\alpha}$ with a restricted signature containing only subs…

Let ${\mathfrak B}$ be an atomless Boolean algebra, let $\alpha$ be an infinite ordinal, and let ${\mathfrak A}$ be the polyadic algebra constructed from a Stone representation of…