The product of two $\textbf {Alt}$ logics possesses the polynomial product finite model property and its membership problem is $\textbf {coNP}$-complete. Using a reduction from an undecidable domino-tiling problem, we prove that its admissibility problem is undecidable.

We prove that $\textbf {K}5$ and some of its extensions that do not contain $\textbf {K}4$ are of unification type $1$.