{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T14:00:42Z","timestamp":1754488842042},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3969,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1996,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 Schr\u00f6dinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.<\/jats:p><jats:p>Mathematics Subject Classification: 03E35, 81P10, 03E25, 35Q40, 46B26, 47A60.<\/jats:p>","DOI":"10.1002\/malq.19960420128","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:48:04Z","timestamp":1180201684000},"page":"319-340","source":"Crossref","is-referenced-by-count":4,"title":["The Axiom of Choice in Quantum Theory"],"prefix":"10.1002","volume":"42","author":[{"given":"Norbert","family":"Brunner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karl","family":"Svozil","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias","family":"Baaz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.522953"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/1968621"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093635333"},{"key":"e_1_2_1_5_2","first-page":"1","article-title":"Linear operators and Dedekind sets","volume":"31","author":"Brunner N.","year":"1986","journal-title":"Math. 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