EFFECTIVE QUANTUM OBSERVABLES

We construct a quantum-theoretic formalism which is meaningful also in the absence of the axiom of choice. In terms of the standard formalis m the observables correspond to the intrinsically effective Hamiltonia ns. Here a self-adjoint operator is intrinsically effective iff the Sc hrodinger equation of its generated semigroup is soluble by means of e igenfunction series expansions. As an application we investigate quant um theory in models of set theory, where the axiom of choice is violat ed. We explain the failure of the axiom of choice in terms of symmetry properties of the perceivable concepts of an external observer who ap plies these concepts in the description of quantum-theoretic experimen tal configurations.