Quantum axiomatics and a theorem of M. P. Soler

Three of the traditional quantum axioms (orthocomplementation, orthomodular ity, and the covering law) show incompatibilities with two products introdu ced by Aerts for the description of joint entities. Inspired by Soler's the orem and Holland's AUG axiom, we propose a property of 'plane transitivity, ' which also characterizes classical Hilbert spaces among infinite-dimensio nal orthomodular spaces, as a possible partial substitute for the 'defectiv e' axioms.