{"id":"https://openalex.org/W4231629838","doi":"https://doi.org/10.2307/2267043","title":"Nicht konstruktiv beweisbare S\u00e4tze der Analysis","display_name":"Nicht konstruktiv beweisbare S\u00e4tze der Analysis","publication_year":1949,"publication_date":"1949-09-01","ids":{"openalex":"https://openalex.org/W4231629838","doi":"https://doi.org/10.2307/2267043"},"language":"de","primary_location":{"id":"doi:10.2307/2267043","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267043","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":null,"display_name":"Ernst Specker","orcid":null},"institutions":[{"id":"https://openalex.org/I2799323385","display_name":"Board of the Swiss Federal Institutes of Technology","ror":"https://ror.org/01rvn4p91","country_code":"CH","type":"government","lineage":["https://openalex.org/I2799323385"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Ernst Specker","raw_affiliation_strings":["Eidg. Techn. Hochschule, Z\u00fcrich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eidg. Techn. Hochschule, Z\u00fcrich","institution_ids":["https://openalex.org/I2799323385"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I2799323385"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":237,"citation_normalized_percentile":{"value":0.45242718,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"14","issue":"3","first_page":"145","last_page":"158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9692999720573425,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9546999931335449,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.47866711020469666},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.4425353407859802},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3901744484901428}],"concepts":[{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.47866711020469666},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.4425353407859802},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3901744484901428}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2267043","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267043","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1993151226","https://openalex.org/W2004839050","https://openalex.org/W2017136603","https://openalex.org/W2023778211","https://openalex.org/W2126160338","https://openalex.org/W2323777246"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049"],"abstract_inverted_index":{"Nach":[0],"allgemeiner":[1],"Ueberzeugung":[2],"k\u00f6nnen":[3],"gewisse":[4],"S\u00e4tze":[5],"der":[6,67,118,133,144,147,197,307],"Analysis":[7,120],"nicht":[8,125,297,312],"konstruktiv":[9,126,313],"bewiesen":[10,127,314],"werden.":[11],"Man":[12],"denke":[13],"etwa":[14,50,170],"an":[15],"den":[16,96],"folgenden":[17,113],"Satz:":[18],"Eine":[19,221,256],"monotone":[20,290],"und":[21,146,151,173,242,252,291],"beschr\u00e4nkte":[22,292],"Folge":[23,68,90,222,257,293],"a":[24,69,91],"(":[25,62,70,92,105,276],"n":[26,71,93,226,237,240,244,249,259],")":[27,64,72,94,107,227,241,245,250,260,278],"von":[28,114,183,261],"rationalen":[29,262],"Zahlen":[30,224,263],"konvergiert,":[31],"d.h.":[32],"es":[33,85,231,269],"gibt":[34,287],"eine":[35,100,163,270,288],"solche":[36,232,271],"ganzzahlige":[37],"Funktion":[38,60,160,166,274],"k(m)":[39],",":[40],"da\u00df":[41,84,123,247,280,306],"Unter":[42,157],"einem":[43],"konstruktiven":[44],"Beweis":[45,79],"dieses":[46],"Satzes":[47],"h\u00e4tte":[48],"man":[49],"die":[51,59,142,203,211,296],"Angabe":[52],"eines":[53],"Verfahrens":[54],"zu":[55,74,86,308],"verstehen,":[56],"das":[57],"gestattet,":[58],"k":[61,104],"m":[63,106,277],"auf":[65,141],"Grand":[66],"rekursiv":[73,88,101,265],"definieren.":[75],"Wenn":[76],"ein":[77],"solcher":[78],"vorl\u00e4ge,":[80],"w\u00e4re":[81],"insbesondere":[82],"gezeigt,":[83],"einer":[87,158],"definierten":[89,199],"mit":[95],"verlangten":[97],"Eigenschaften":[98],"stets":[99],"definierbare":[102],"Konvergenzfunktion":[103],"gibt.":[108],"Es":[109,286],"soil":[110],"nun":[111],"im":[112,181],"einigen":[115],"grundlegenden":[116],"S\u00e4tzen":[117],"reellen":[119],"gezeigt":[121],"werden,":[122],"sie":[124],"werden":[128,168,282,315],"k\u00f6nnen\u2014konstruktiv":[129],"in":[130],"dem":[131],"Sinn,":[132],"eben":[134],"angedeutet":[135],"wurde.":[136],"Wir":[137,281],"st\u00fctzen":[138],"uns":[139],"dabei":[140],"Begriffe":[143],"rekursiven":[145,159,233],"berechenbaren":[148],"Funktion;":[149],"rekursive":[150,165,272],"berechenbare":[152],"Funktionen":[153,235],"sind":[154],"zahlentheoretische":[155],"Funktionen.":[156],"m\u00f6ge":[161],"vorl\u00e4ufig":[162],"primitiv":[164],"verstanden":[167],"(vgl.":[169],"D.":[171],"Hilbert":[172],"P.":[174],"Bernays":[175],"[3],":[176],"S.286);":[177],"berechenbar":[178,180,298],"meint":[179],"Sinne":[182],"A.":[184,191],"Church":[185],"[1],":[186],"S.":[187],"C.":[188],"Kleene":[189],"[4],":[190],"M.":[192],"Turing":[193],"[6].":[194],"Der":[195],"Begriff":[196],"\u201ckonstruktiv":[198],"Funktion\u201d":[200,207,215],"wird":[201],"durch":[202,210],"Bestimmung":[204,212],"als":[205,213],"\u201crekursive":[206],"eher":[208,216],"eng,":[209],"\u201cberechenbare":[214],"weit":[217],"gefa\u00dft.":[218],"Definition":[219,254],"I.":[220],"rationaler":[223,294],"\u03a6(":[225,258],"hei\u00dft":[228,264],"rekursiv,(berechenbar),":[229],"wenn":[230,268],"(berechenbaren)":[234],"\u03d5{":[236],"),":[238],"\u03c8(":[239],"\u03c7(":[243,248],"gibt,":[246,279],"\u22671":[251],".":[253],"II.":[255],"(berechenbar)":[266],"konvergent,":[267],"(berechenbare)":[273],"v":[275],"zeigen":[283],"(Satz":[284],"I):":[285],"rekursive,":[289],"Zahlen,":[295],"konvergiert.":[299],"Bei":[300],"unserer":[301],"Auffassungsweise":[302],"ist":[303],"darin":[304],"enthalten,":[305],"Beginn":[309],"erw\u00e4hnte":[310],"Satz":[311],"kann.":[316]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2026-07-11T18:08:03.149640","created_date":"2025-10-10T00:00:00"}