{"id":"https://openalex.org/W2073450814","doi":"https://doi.org/10.1002/malq.19960420128","title":"The Axiom of Choice in Quantum Theory","display_name":"The Axiom of Choice in Quantum Theory","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2073450814","doi":"https://doi.org/10.1002/malq.19960420128","mag":"2073450814"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19960420128","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19960420128","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034039240","display_name":"Norbert Brunner","orcid":"https://orcid.org/0000-0001-6487-5752"},"institutions":[{"id":"https://openalex.org/I137696358","display_name":"Gregor Mendel Institute of Molecular Plant Biology","ror":"https://ror.org/05twjp994","country_code":"AT","type":"facility","lineage":["https://openalex.org/I137696358","https://openalex.org/I138211613","https://openalex.org/I4210142901"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Norbert Brunner","raw_affiliation_strings":["Institut fu\u0308r Mathematik, Universita\u0308t fu\u0308r Bodenkultur, Gregor-Mendel-Stra\u00dfe 33, A-1080 Wien, Austria","Institut f\u00fcr Mathematik, Universit\u00e4t f\u00fcr Bodenkultur, Gregor\u2010Mendel\u2010Stra\u00dfe 33, A\u20101080 Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut fu\u0308r Mathematik, Universita\u0308t fu\u0308r Bodenkultur, Gregor-Mendel-Stra\u00dfe 33, A-1080 Wien, Austria","institution_ids":["https://openalex.org/I137696358"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t f\u00fcr Bodenkultur, Gregor\u2010Mendel\u2010Stra\u00dfe 33, A\u20101080 Wien, Austria","institution_ids":["https://openalex.org/I137696358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048189936","display_name":"Karl Svozil","orcid":"https://orcid.org/0000-0001-6554-2802"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Karl Svozil","raw_affiliation_strings":["Institut fu\u0308r Theoretische Physik, TU Wien, Wiedner Hauptstra\u00dfe 8 \u2013 10, A-1040 Wien, Austria","Institut f\u00fcr Theoretische Physik, TU Wien, Wiedner Hauptstra\u00dfe 8 \u2013 10, A\u20101040 Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut fu\u0308r Theoretische Physik, TU Wien, Wiedner Hauptstra\u00dfe 8 \u2013 10, A-1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik, TU Wien, Wiedner Hauptstra\u00dfe 8 \u2013 10, A\u20101040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035315045","display_name":"Matthias Baaz","orcid":"https://orcid.org/0000-0002-7815-2501"},"institutions":[{"id":"https://openalex.org/I119444370","display_name":"Papua New Guinea University of Technology","ror":"https://ror.org/012g45386","country_code":"PG","type":"education","lineage":["https://openalex.org/I119444370"]},{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT","PG"],"is_corresponding":true,"raw_author_name":"Matthias Baaz","raw_affiliation_strings":["Abteilung Theoretische Informatik, TU Wien, Wiedner Hauptstra\u00dfe 8 \u2013 10, A-1040 Wien, Austria","The results of our paper have been presented in June 1992 at a conference of the DVMLGdM at Mu\u0308nster, 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 \u201cget 9501018\u201d to the data base \u201cquant-ph@xxx.lanl.gov\u201d. The authors gratefully remember helpful comments by professors Ruppert (University of Bodenkultur) and Schachermayer (University of Vienna)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abteilung Theoretische Informatik, TU Wien, Wiedner Hauptstra\u00dfe 8 \u2013 10, A-1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"The results of our paper have been presented in June 1992 at a conference of the DVMLGdM at Mu\u0308nster, 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 \u201cget 9501018\u201d to the data base \u201cquant-ph@xxx.lanl.gov\u201d. The authors gratefully remember helpful comments by professors Ruppert (University of Bodenkultur) and Schachermayer (University of Vienna)","institution_ids":["https://openalex.org/I119444370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035315045"],"corresponding_institution_ids":["https://openalex.org/I119444370","https://openalex.org/I145847075"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.22659927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"42","issue":"1","first_page":"319","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8443082571029663},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.7258113026618958},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6689592599868774},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6351503729820251},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6165913939476013},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.6125844717025757},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.5991315245628357},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5319687724113464},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.49440550804138184},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4662225544452667},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.46369776129722595},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4438946843147278},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3344005346298218},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3039589524269104},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.19217351078987122},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.16275811195373535},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07651230692863464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06590569019317627},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.0653088390827179}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8443082571029663},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.7258113026618958},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6689592599868774},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6351503729820251},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6165913939476013},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.6125844717025757},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.5991315245628357},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5319687724113464},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.49440550804138184},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4662225544452667},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.46369776129722595},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4438946843147278},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3344005346298218},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3039589524269104},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19217351078987122},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.16275811195373535},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07651230692863464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06590569019317627},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0653088390827179},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19960420128","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19960420128","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W4111744","https://openalex.org/W591591544","https://openalex.org/W1551313231","https://openalex.org/W1585255196","https://openalex.org/W1967842301","https://openalex.org/W1990165314","https://openalex.org/W1996686235","https://openalex.org/W2033599456","https://openalex.org/W2058996432","https://openalex.org/W2069535152","https://openalex.org/W2076687762","https://openalex.org/W2089716787","https://openalex.org/W2896297313","https://openalex.org/W3003414507","https://openalex.org/W3040996531","https://openalex.org/W3126996113","https://openalex.org/W3173263824","https://openalex.org/W4253191968","https://openalex.org/W4255057637","https://openalex.org/W4299138315","https://openalex.org/W6642290154"],"related_works":["https://openalex.org/W3034881686","https://openalex.org/W2031083694","https://openalex.org/W423103167","https://openalex.org/W1574825745","https://openalex.org/W288388583","https://openalex.org/W2979076867","https://openalex.org/W2491940682","https://openalex.org/W2061896392","https://openalex.org/W1504849543","https://openalex.org/W2045975809"],"abstract_inverted_index":{"Abstract":[0],"We":[1,13],"construct":[2],"peculiar":[3],"Hilbert":[4],"spaces":[5],"from":[6],"counterexamples":[7],"to":[8],"the":[9,15,43],"axiom":[10],"of":[11,22,46,54],"choice.":[12],"identify":[14],"intrinsically":[16,37],"effective":[17,38],"Hamiltonians":[18],"with":[19,28],"those":[20],"observables":[21],"quantum":[23],"theory":[24],"which":[25],"may":[26],"coexist":[27],"such":[29],"spaces.":[30],"Here":[31],"a":[32],"self":[33],"adjoint":[34],"operator":[35],"is":[36,50],"if":[39,42],"and":[40],"only":[41],"Schr\u00f6dinger":[44],"equation":[45],"its":[47],"generated":[48],"semigroup":[49],"soluble":[51],"by":[52],"means":[53],"eigenfunction":[55],"series":[56],"expansions.":[57],"Mathematics":[58],"Subject":[59],"Classification:":[60],"03E35,":[61],"81P10,":[62],"03E25,":[63],"35Q40,":[64],"46B26,":[65],"47A60.":[66]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}