Three Classes of Orthomodular Lattices

Abstract

Let $$\mathcal{OML}$$ denote the class of all orthomodular lattices and $$\mathcal{C}$$ denote the class of those that are commutator-finite. Also, let $$\mathcal{C}_{1}$$ denote the class of orthomodular lattices that satisfy the block extension property, $$\mathcal{C}_{2}$$ those that satisfy the weak block extension property, and $$\mathcal{C}_{3}$$ those that are locally finite. We show that the following strict containments hold: $$\mathcal{C} \subset \mathcal{C}_{1} \subset \mathcal{C}_{2} \subset \mathcal{C}_{3} \subset \mathcal{OML}.$$