Algebraic lattices are complete sublattices of the clone lattice over an infinite set
Volume 195 / 2007
Fundamenta Mathematicae 195 (2007), 1-10
MSC: Primary 08A40; Secondary 08A05.
DOI: 10.4064/fm195-1-1
Abstract
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 $\mathop{\rm Cl}(X)$.
