# Effective quantum observables

@article{Brunner1995EffectiveQO, title={Effective quantum observables}, author={Norbert Brunner and Karl Svozil and Matthias Baaz}, journal={Il Nuovo Cimento B (1971-1996)}, year={1995}, volume={110}, pages={1397-1413} }

SummaryWe construct a quantum-theoretic formalism which is meaningful also in the absence of the axiom of choice. In terms of the standard formalism the observables correspond to the intrinsically effective Hamiltonians. Here a self-adjoint operator is intrinsically effective iff the Schrödinger equation of its generated semigroup is soluble by means of eigenfunction series expansions. As an application we investigate quantum theory in models of set theory, where the axiom of choice is violated…

## 4 Citations

The Baire Category Property and Some Notions of Compactness

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- 1998

We work in set theory without the axiom of choice: ZF. We show that the axiom BC: Compact Hausdorff spaces are Baire, is equivalent to the following axiom: Every tree has a subtree whose levels are…

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There is a reasonable, nondictatorial social welfare function satisfying "finite discrimination", if and only if in Weglorz' model there is a free ultrafilter on a set representing the individuals.

Choice principles in Węglorz’ models

- Mathematics
- 2007

Węglorz’ models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the…

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