{"id":"https://openalex.org/W2087408122","doi":"https://doi.org/10.1016/0168-0072(86)90066-7","title":"Which set existence axioms are needed to prove the separable Hahn-Banach theorem?","display_name":"Which set existence axioms are needed to prove the separable Hahn-Banach theorem?","publication_year":1986,"publication_date":"1986-01-01","ids":{"openalex":"https://openalex.org/W2087408122","doi":"https://doi.org/10.1016/0168-0072(86)90066-7","mag":"2087408122"},"language":"en","primary_location":{"id":"doi:10.1016/0168-0072(86)90066-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(86)90066-7","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied 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/A5033975476","display_name":"Douglas K. Brown","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Douglas K. Brown","raw_affiliation_strings":["Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA","Department of Mathematics; The Pennsylvania State University; University Park PA 16802 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Mathematics; The Pennsylvania State University; University Park PA 16802 USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110459430","display_name":"Stephen G. Simpson","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen G. Simpson","raw_affiliation_strings":["Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA","Department of Mathematics; The Pennsylvania State University; University Park PA 16802 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Mathematics; The Pennsylvania State University; University Park PA 16802 USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033975476"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":1.9698,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.86688367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"31","issue":null,"first_page":"123","last_page":"144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9714000225067139,"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":0.9714000225067139,"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/mathematics","display_name":"Mathematics","score":0.8880591988563538},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.7918182611465454},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.6855760216712952},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5919144749641418},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5820616483688354},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5795711874961853},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5309960842132568},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.5298652052879333},{"id":"https://openalex.org/keywords/eberlein\u2013\u0161mulian-theorem","display_name":"Eberlein\u2013\u0160mulian theorem","score":0.5193372964859009},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.45675525069236755},{"id":"https://openalex.org/keywords/banach-manifold","display_name":"Banach manifold","score":0.4321715235710144},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38130685687065125},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.21820896863937378},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.18338057398796082},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10095450282096863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8880591988563538},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.7918182611465454},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6855760216712952},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5919144749641418},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5820616483688354},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5795711874961853},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5309960842132568},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.5298652052879333},{"id":"https://openalex.org/C184908153","wikidata":"https://www.wikidata.org/wiki/Q2226650","display_name":"Eberlein\u2013\u0160mulian theorem","level":4,"score":0.5193372964859009},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.45675525069236755},{"id":"https://openalex.org/C165593952","wikidata":"https://www.wikidata.org/wiki/Q3554819","display_name":"Banach manifold","level":4,"score":0.4321715235710144},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38130685687065125},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.21820896863937378},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.18338057398796082},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10095450282096863},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0168-0072(86)90066-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(86)90066-7","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W7980256","https://openalex.org/W35119461","https://openalex.org/W78146983","https://openalex.org/W83512845","https://openalex.org/W597708701","https://openalex.org/W627811487","https://openalex.org/W1027937706","https://openalex.org/W1491173026","https://openalex.org/W1522998756","https://openalex.org/W1539702044","https://openalex.org/W2010586901","https://openalex.org/W2038447110","https://openalex.org/W2060878518","https://openalex.org/W2106260240","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W4210931879","https://openalex.org/W6600317676","https://openalex.org/W6601469024","https://openalex.org/W6603233204","https://openalex.org/W6603397711","https://openalex.org/W6626632686","https://openalex.org/W6688240227","https://openalex.org/W6808814299","https://openalex.org/W7074219214"],"related_works":["https://openalex.org/W2047711809","https://openalex.org/W2116579313","https://openalex.org/W2134310526","https://openalex.org/W2787144471","https://openalex.org/W2086608401","https://openalex.org/W4213356241","https://openalex.org/W2593141400","https://openalex.org/W2967076817","https://openalex.org/W1559682655","https://openalex.org/W3197871941"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}