Quantum Axiomatics and a Theorem of M. P. Solèr
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Three of the traditional quantum axioms (orthocomplementation, orthomodularity,and the covering law) show incompatibilities with two products introduced byAerts for the description of joint entities. Inspired by Solèr's theorem and Holland'sAUG axiom, we propose a property of 'plane transitivity,' which also characterizesclassical Hilbert spaces among infinite-dimensional orthomodular spaces, as apossible partial substitute for the 'defective' axioms.
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