QUASIBOOLEAN ALGEBRAS AND SIMULTANEOUSLY DEFINITE PROPERTIES IN QUANTUM-MECHANICS

We define and characterize a new abstract notion of ''quasiBoolean alg ebra,'' intermediate in nature between an (ortho)lattice and a Boolean algebra. It will turn out that such algebras are natural candidates f or representing the simultaneously definite properties of a quantum sy stem. We then prove a general theorem about maximal quasiBoolean subal gebras of an ortholattice which we use to derive a number of different proposals in the literature for what properties of a quantum system s hould be regarded as simultaneously definite.