  An irreducible complete atomic OML of infinite height cannot both be
algebraic and have the covering property. However, Kalmbach's construction
provides an example of such an OML that is algebraic and has the 2-covering
property, and Keller's construction provides an example of such an OML that has
the covering property and is completely hereditarily atomic. Completely
hereditarily atomic OMLs generalize algebraic OMLs suitably to quantum
predicate logic.
