{"id":"https://openalex.org/W2801357573","doi":"https://doi.org/10.1002/malq.201600041","title":"Bishop's Lemma","display_name":"Bishop's Lemma","publication_year":2018,"publication_date":"2018-04-01","ids":{"openalex":"https://openalex.org/W2801357573","doi":"https://doi.org/10.1002/malq.201600041","mag":"2801357573"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201600041","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201600041","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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/A5086209658","display_name":"Hannes Diener","orcid":"https://orcid.org/0000-0002-1122-5753"},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Hannes Diener","raw_affiliation_strings":["School of Mathematics and Statistics University of Canterbury Private Bag 4800 Christchurch 8140 New Zealand","School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, 8140 New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics University of Canterbury Private Bag 4800 Christchurch 8140 New Zealand","institution_ids":["https://openalex.org/I185492890"]},{"raw_affiliation_string":"School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, 8140 New Zealand","institution_ids":["https://openalex.org/I185492890"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112641240","display_name":"Matthew Hendtlass","orcid":null},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Matthew Hendtlass","raw_affiliation_strings":["School of Mathematics and Statistics University of Canterbury Private Bag 4800 Christchurch 8140 New Zealand","School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, 8140 New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics University of Canterbury Private Bag 4800 Christchurch 8140 New Zealand","institution_ids":["https://openalex.org/I185492890"]},{"raw_affiliation_string":"School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, 8140 New Zealand","institution_ids":["https://openalex.org/I185492890"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086209658"],"corresponding_institution_ids":["https://openalex.org/I185492890"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03783704,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"1-2","first_page":"49","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11349","display_name":"Music Technology and Sound Studies","score":0.8367000222206116,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11349","display_name":"Music Technology and Sound Studies","score":0.8367000222206116,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10941","display_name":"Musicology and Musical Analysis","score":0.8093000054359436,"subfield":{"id":"https://openalex.org/subfields/1210","display_name":"Music"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12398","display_name":"Poetry Analysis and Criticism","score":0.7978000044822693,"subfield":{"id":"https://openalex.org/subfields/1208","display_name":"Literature and Literary Theory"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.9729106426239014},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8457134962081909},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6994509100914001},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6346572041511536},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.5335498452186584},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5104581117630005},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.4697440266609192},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.4427124857902527},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40404051542282104},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37542667984962463},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.37454915046691895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33263444900512695},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.1382754147052765},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.07032054662704468},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.058971911668777466},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0568641722202301},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0488990843296051},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.04350516200065613}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.9729106426239014},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8457134962081909},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6994509100914001},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6346572041511536},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.5335498452186584},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5104581117630005},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4697440266609192},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.4427124857902527},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40404051542282104},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37542667984962463},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.37454915046691895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33263444900512695},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.1382754147052765},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.07032054662704468},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.058971911668777466},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0568641722202301},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0488990843296051},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.04350516200065613},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.201600041","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201600041","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W177158136","https://openalex.org/W1505480266","https://openalex.org/W1590304156","https://openalex.org/W1972516737","https://openalex.org/W1988237188","https://openalex.org/W2017384344","https://openalex.org/W2067914884","https://openalex.org/W2072152180","https://openalex.org/W4239316923","https://openalex.org/W4254994720"],"related_works":["https://openalex.org/W3109582549","https://openalex.org/W2949665548","https://openalex.org/W1608708592","https://openalex.org/W2142305280","https://openalex.org/W3186402499","https://openalex.org/W1481154196","https://openalex.org/W2063422058","https://openalex.org/W2606121466","https://openalex.org/W4377158283","https://openalex.org/W201195458"],"abstract_inverted_index":{"Abstract":[0],"Bishop's":[1,31,47],"Lemma":[2,32,48],"is":[3,39],"a":[4,40],"centrepiece":[5],"in":[6,30],"the":[7,21,27],"development":[8],"of":[9,20,23,43],"constructive":[10],"analysis.":[11],"We":[12],"show":[13],"that":[14,26,37,46],"its":[15],"proof":[16],"requires":[17],"some":[18],"form":[19],"axiom":[22],"choice;":[24],"and":[25,36],"completeness":[28],"requirement":[29],"can":[33],"be":[34],"weakened":[35],"there":[38],"vast":[41],"class":[42],"non\u2010complete":[44],"spaces":[45],"applies":[49],"to.":[50]},"counts_by_year":[],"updated_date":"2026-07-07T14:30:12.667765","created_date":"2018-05-17T00:00:00"}
