{"id":"https://openalex.org/W2166399063","doi":"https://doi.org/10.1017/s002248120003944x","title":"Ueber eine abgeschwaechte Fassung des Auswahlaxioms","display_name":"Ueber eine abgeschwaechte Fassung des Auswahlaxioms","publication_year":1937,"publication_date":"1937-03-01","ids":{"openalex":"https://openalex.org/W2166399063","doi":"https://doi.org/10.1017/s002248120003944x","mag":"2166399063"},"language":"de","primary_location":{"id":"doi:10.1017/s002248120003944x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s002248120003944x","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5110140567","display_name":"A. Fraenkel","orcid":null},"institutions":[{"id":"https://openalex.org/I129975664","display_name":"Albert Einstein College of Medicine","ror":"https://ror.org/05cf8a891","country_code":"US","type":"education","lineage":["https://openalex.org/I129975664","https://openalex.org/I4210112371"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["BG","CZ","IL","US"],"is_corresponding":true,"raw_author_name":"A. Fraenkel","raw_affiliation_strings":["Einstein Institute of Mathematics, Hebrew University, Jerusalem"],"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, Hebrew University, Jerusalem","institution_ids":["https://openalex.org/I197251160","https://openalex.org/I4210105926","https://openalex.org/I4210120266","https://openalex.org/I129975664"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110140567"],"corresponding_institution_ids":["https://openalex.org/I129975664","https://openalex.org/I197251160","https://openalex.org/I4210105926","https://openalex.org/I4210120266"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.24556962,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","issue":"1","first_page":"1","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9391000270843506,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9391000270843506,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.9052000045776367,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.6683824062347412},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.48730576038360596},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34016937017440796}],"concepts":[{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.6683824062347412},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.48730576038360596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34016937017440796}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s002248120003944x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s002248120003944x","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183142177","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183142177","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W930256190","https://openalex.org/W943508897","https://openalex.org/W1975810242","https://openalex.org/W1991697528","https://openalex.org/W2004839050","https://openalex.org/W2045439583","https://openalex.org/W2087264266"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2780307509","https://openalex.org/W2609344916","https://openalex.org/W2478882070","https://openalex.org/W59019880","https://openalex.org/W2308060692","https://openalex.org/W4210390885"],"abstract_inverted_index":{"Einleitung":[0],".":[1],"Das":[2],"\u201cAuswahlaxiom\u201d":[3],"oder":[4,75,81],"\u201cmultiplicative":[5],"axiom\u201d":[6],"fordert":[7],"in":[8,90,207,237,251],"der":[9,71,100,141,246,260,265],"gew\u00f6hnlichen,":[10],"von":[11,40,102,153,194,215,225],"B.":[12,204],"Russell":[13],"und":[14,28,49,127,163],"Zermelo":[15],"angegebenen":[16],"Fassung,":[17],"da\u00df":[18,65,111],"zu":[19,61,109,130,134],"jeder":[20],"Menge":[21,72,142,214],"M":[22,41,73,103,154,158,190,195,211,226],",":[23,74,156],"deren":[24],"Elemente":[25,193,224,236],"paarweise":[26],"fremde":[27],"nicht-leere":[29],"Mengen":[30,197],"sind,":[31,202],"mindestens":[32],"eine":[33,212,228],"\u201cAuswahlmenge\u201d":[34],"existiere,":[35],"die":[36,58,69,77,94,107,139,149,159,180,192,223,232,233],"mit":[37,198],"jedem":[38],"Element":[39,44],"genau":[42],"\u00e9in":[43],"gemeinsam":[45],"hat.":[46],"Die":[47,240],"n\u00e4chstliegende":[48],"mehrfach":[50],"verwendete":[51],"Methode,":[52],"um":[53],"ein":[54],"schw\u00e4cheres":[55],"Postulat":[56],"als":[57],"vorstehende":[59],"Fassung":[60],"formulieren,":[62],"besteht":[63],"darin,":[64],"man":[66],"entweder":[67],"\u00fcber":[68,76,82],"M\u00e4chtigkeit":[70,101,160],"M\u00e4chtigkeiten":[78,199],"ihrer":[79],"Elemente,":[80],"beides":[83],"gleichzeitig,":[84],"einschr\u00e4nkende":[85],"Bedingungen":[86],"macht,":[87],"also":[88,205],"nur":[89],"diesen":[91],"eingeschr\u00e4nkten":[92],"F\u00e4llen":[93],"Existenz":[95,150,181],"einer":[96,151,174,182],"Auswahlmenge":[97,152,183],"verlangt.":[98],"Hinsichtlich":[99],"ist":[104,147,179,255],"da":[105],"sogleich":[106],"Bemerkung":[108],"machen,":[110],"sie":[112],"jedenfalls":[113],"transfinit":[114],"(genauer:":[115],"nicht":[116,184,227],"endlich":[117],"im":[118],"induktiven":[119],"Sinn)":[120],"anzusetzen":[121],"ist.":[122],"Verm\u00f6ge":[123],"allgemeiner":[124],"logischer":[125],"Sachverhalte":[126],"des":[128,248,262],"(eventuell":[129],"beweisenden)":[131],"Prinzips,":[132],"das":[133],"einem":[135],"gegebenen":[136],"Objekt":[137],"a":[138,144],"Bildung":[140],"{":[143],"}":[145],"erlaubt,":[146],"n\u00e4mlich":[148],"beweisbar":[155],"falls":[157],"1":[161,201],"besitzt,":[162],"diese":[164],"Beweisbarkeit":[165],"\u00fcbertr\u00e4gt":[166],"sich":[167],"mittels":[168],"gew\u00f6hnlicher":[169],"Induktion":[170],"auf":[171,259],"den":[172],"Fall":[173],"beliebigen":[175],"endlichen":[176],"M\u00e4chtigkeit.":[177],"Dagegen":[178],"mehr":[185],"beweisbar,":[186],"wenn":[187,222],"(bei":[188],"transfinitem":[189],")":[191],"endliche":[196],">":[200],"z.":[203],"schon":[206],"dem":[208],"Fall,":[209,254],"wo":[210],"transfinite":[213],"Paaren":[216],"ist\u2014nat\u00fcrlich":[217],"\u201cim":[218],"allgemeinen,\u201d":[219],"d.":[220,244],"h.":[221,245],"besondere":[229],"Beschaffenheit":[230],"haben,":[231],"Auszeichnung":[234],"gewisser":[235],"ihnen":[238],"erm\u00f6glicht.":[239],"Tatsache":[241],"dieser":[242],"Nichtbeweisbarkeit,":[243],"Unabh\u00e4ngigkeit":[247],"Auswahlaxioms":[249],"sogar":[250],"diesem":[252],"einfachsten":[253],"vor":[256],"l\u00e4ngerer":[257],"Zeit":[258],"Basis":[261],"Zermeloschen":[263],"Axiomensystems":[264],"Mengenlehre":[266],"nachgewiesen":[267],"worden.":[268]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}