{"id":"https://openalex.org/W2031083694","doi":"https://doi.org/10.1002/malq.200410052","title":"Properties of the real line and weak forms of the Axiom of Choice","display_name":"Properties of the real line and weak forms of the Axiom of Choice","publication_year":2005,"publication_date":"2005-09-28","ids":{"openalex":"https://openalex.org/W2031083694","doi":"https://doi.org/10.1002/malq.200410052","mag":"2031083694"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200410052","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410052","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":"MLQ","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/A5028328758","display_name":"Omar De la Cruz","orcid":"https://orcid.org/0000-0001-9489-4647"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Omar De la Cruz","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA","Department of Mathematics , Purdue University , West Lafayette , IN 47907 , USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Department of Mathematics , Purdue University , West Lafayette , IN 47907 , USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101476392","display_name":"Eric Hall","orcid":"https://orcid.org/0000-0001-6159-7494"},"institutions":[{"id":"https://openalex.org/I75421653","display_name":"University of Missouri\u2013Kansas City","ror":"https://ror.org/01w0d5g70","country_code":"US","type":"education","lineage":["https://openalex.org/I75421653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Hall","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Missouri, Kansas City, MO 64110, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Missouri, Kansas City, MO 64110, USA","institution_ids":["https://openalex.org/I75421653"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108590548","display_name":"Paul C. Howard","orcid":null},"institutions":[{"id":"https://openalex.org/I138216421","display_name":"Eastern Michigan University","ror":"https://ror.org/02ehshm78","country_code":"US","type":"education","lineage":["https://openalex.org/I138216421"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Howard","raw_affiliation_strings":["Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA","Department of Mathematics Eastern Michigan University Ypsilanti, MI 48197 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA","institution_ids":["https://openalex.org/I138216421"]},{"raw_affiliation_string":"Department of Mathematics Eastern Michigan University Ypsilanti, MI 48197 USA","institution_ids":["https://openalex.org/I138216421"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028285276","display_name":"Kyriakos Keremedis","orcid":"https://orcid.org/0000-0001-8453-3477"},"institutions":[{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Kyriakos Keremedis","raw_affiliation_strings":["Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece","Department of Mathematics; University of the Aegean; Karlovassi 83200 Samos Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece","institution_ids":["https://openalex.org/I98805295"]},{"raw_affiliation_string":"Department of Mathematics; University of the Aegean; Karlovassi 83200 Samos Greece","institution_ids":["https://openalex.org/I98805295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000502133","display_name":"Eleftherios Tachtsis","orcid":"https://orcid.org/0000-0001-9114-3661"},"institutions":[{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Eleftherios Tachtsis","raw_affiliation_strings":["Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece","Department of Statistics, and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, 83200, Samos, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece","institution_ids":["https://openalex.org/I98805295"]},{"raw_affiliation_string":"Department of Statistics, and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, 83200, Samos, Greece","institution_ids":["https://openalex.org/I98805295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5028328758"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12386742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"51","issue":"6","first_page":"598","last_page":"609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.9761000275611877,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9265999794006348,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/axiom-of-choice","display_name":"Axiom of choice","score":0.975723385810852},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.9461029767990112},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.8687536120414734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8298519849777222},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6797575354576111},{"id":"https://openalex.org/keywords/constructive-set-theory","display_name":"Constructive set theory","score":0.6760468482971191},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.5910915732383728},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5398276448249817},{"id":"https://openalex.org/keywords/axiom-independence","display_name":"Axiom independence","score":0.5169991254806519},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4591464698314667},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3581653833389282},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3259545564651489},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.2792801558971405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09718510508537292},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04513972997665405}],"concepts":[{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.975723385810852},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.9461029767990112},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.8687536120414734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8298519849777222},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6797575354576111},{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.6760468482971191},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.5910915732383728},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5398276448249817},{"id":"https://openalex.org/C170088968","wikidata":"https://www.wikidata.org/wiki/Q4830547","display_name":"Axiom independence","level":3,"score":0.5169991254806519},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4591464698314667},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3581653833389282},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3259545564651489},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2792801558971405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09718510508537292},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04513972997665405},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200410052","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410052","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":"MLQ","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":21,"referenced_works":["https://openalex.org/W70138447","https://openalex.org/W245573756","https://openalex.org/W409372930","https://openalex.org/W1032030852","https://openalex.org/W1132673866","https://openalex.org/W1506329803","https://openalex.org/W1541012876","https://openalex.org/W1608084331","https://openalex.org/W1978413491","https://openalex.org/W1997784525","https://openalex.org/W2003288973","https://openalex.org/W2009467409","https://openalex.org/W2016396872","https://openalex.org/W2028322461","https://openalex.org/W2031917340","https://openalex.org/W2034914951","https://openalex.org/W2035802665","https://openalex.org/W2063858946","https://openalex.org/W2147242351","https://openalex.org/W2323053796","https://openalex.org/W2947556356"],"related_works":["https://openalex.org/W288388583","https://openalex.org/W2350176099","https://openalex.org/W1995120876","https://openalex.org/W2491940682","https://openalex.org/W2796622564","https://openalex.org/W2076278624","https://openalex.org/W2980408391","https://openalex.org/W423103167","https://openalex.org/W207680367","https://openalex.org/W1504849543"],"abstract_inverted_index":{"We":[0],"investigate,":[1],"within":[2],"the":[3,10,16],"framework":[4],"of":[5,15,18,24],"Zermelo-Fraenkel":[6],"set":[7],"theory":[8],"ZF,":[9],"interrelations":[11],"between":[12],"weak":[13],"forms":[14],"Axiom":[17],"Choice":[19],"AC":[20],"restricted":[21],"to":[22],"sets":[23],"reals.":[25],"(\u00a9":[26],"2005":[27],"WILEY-VCH":[28],"Verlag":[29],"GmbH":[30],"&":[31],"Co.":[32],"KGaA,":[33],"Weinheim)":[34]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
