4 problems

Let $\mathsf{SL}_{\infty}$ denote the class of semilattices, and let a filter subclass be a class axiomatized by filter implications. An $n$-adjunction is the implication … A subst…

Let $\mathbf{S}_n$ denote the class of all semilattices of order $n$. For a semilattice $S$, let … where $\mathbf{eq}$ ranges over all equations in one variable and…

Let $L$ be a meet semi-lattice with a fixed linear extension, and let $D$ range over the valid diagrams of $L$, meaning subsets containing the minimal elements and stable under joi…

Let $\alpha$ be a countable chain, and let $\mathbb{B}$ be a set of join-semilattices with least element such that an algebraic lattice $L$ contains no chain of order type…