Algebraic lattices are complete sublattices of the clone lattice over an infinite set
Michael Pinsker · Fundamenta Mathematicae · 2007
The clone lattice $\mathop{\rm Cl}(X)$ over an infinite set $X$ is a complete algebraic lattice with $2^{|X|}$ compact elements. We show that every algebraic lattice with at most $2^{|X|}$ compact elements is a complete sublattice of $\mathop{\rm Cl}(X)$.