A NOTE ON BOOLEAN SUBSETS OF ORTHOMODULAR POSETS

Abstract

Modelling quantum systems by orthomodular posets \(\mathcal{P}\) = (P, ≤, ‘ , 0, 1) gives rise to the question, when a finite subset A of P lies within a Boolean subalgebra of \(\mathcal{P}\), in which case A is called Boolean.  Boolean subsets A specify the physical subsystem represented by A to be classical.  We give a characterization of a subset of P to be Boolean by only taking into account terms of elements of this subset and in such a way that an inductive algorithm can be derived.