Orthocomplemented lattices with a symmetric difference
The central notion of this paper is the so-called orthocomplemented difference lattice (shortly ODL). This is an ortholattice endowed with an additional binary operation (the so-called symmetric difference) satisfying certain axioms. Every ODL induces a corresponding orthomodular lattice. Valuations, set-representable ODLs (shortly SRODLs), several types of ideals as well as horizontal sums of Boolean algebras are considered. SRODLs are characterized by means of the existence of certain valuations respectively ideals and it is shown that the class of all SRODLs forms a variety. Examples of ODLs being not set-representable are given.
scientific article; zbMATH DE number 5652277