The results of our paper have been presented in June 1992 at a conference of the DVMLGdM at Münster, in March 1993 at a meeting of the contact group in mathematical logic at Louvaine de la Neufe, in August 1995 at a LMPS conference at Firenze and at several colloquium talks. A plain TeX file of an extended preliminary version of the paper may be retrieved by sending an e-mail message with the subject “get 9501018” to the data base “firstname.lastname@example.org”. The authors gratefully remember helpful comments by professors Ruppert (University of Bodenkultur) and Schachermayer (University of Vienna).
The Axiom of Choice in Quantum Theory
Article first published online: 13 NOV 2006
Copyright © 1996 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Mathematical Logic Quarterly
Volume 42, Issue 1, pages 319–340, 1996
How to Cite
Brunner, N., Svozil, K. and Baaz, M. (1996), The Axiom of Choice in Quantum Theory. Mathematical Logic Quarterly, 42: 319–340. doi: 10.1002/malq.19960420128
- Issue published online: 13 NOV 2006
- Article first published online: 13 NOV 2006
- Manuscript Received: 30 JUL 1995
- Axiom of multiple choice;
- Fraenkel-Mostowski permutation model;
- Self-adjoint operator;
- Schrödinger equation
We construct peculiar Hilbert spaces from counterexamples to the axiom of choice. We identify the intrinsically effective Hamiltonians with those observables of quantum theory which may coexist with such spaces. Here a self adjoint operator is intrinsically effective if and only if the Schrödinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.
Mathematics Subject Classification: 03E35, 81P10, 03E25, 35Q40, 46B26, 47A60.