{"id":"https://openalex.org/W2027293698","doi":"https://doi.org/10.1002/malq.19950410309","title":"The Set of Better Quasi Orderings is \u220f","display_name":"The Set of Better Quasi Orderings is \u220f","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2027293698","doi":"https://doi.org/10.1002/malq.19950410309","mag":"2027293698"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19950410309","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19950410309","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/A5047796693","display_name":"Alberto Marcone","orcid":"https://orcid.org/0000-0001-8356-0086"},"institutions":[{"id":"https://openalex.org/I1330701686","display_name":"Collegio Carlo Alberto","ror":"https://ror.org/0397knh37","country_code":"IT","type":"education","lineage":["https://openalex.org/I1330701686"]},{"id":"https://openalex.org/I4210111890","display_name":"Tochigi Prefectural Police","ror":"https://ror.org/0182aka86","country_code":"JP","type":"government","lineage":["https://openalex.org/I4210111890"]}],"countries":["IT","JP"],"is_corresponding":true,"raw_author_name":"Alberto Marcone","raw_affiliation_strings":["Dipartimento di Matematica, Universita\u0301 di Torino Via Carlo Alberto 10, I\u201310123 Torino, Italy","I am very much indebted to STEPHEN G. SIMPSON, who introduced me to bqo theory, supervised my Ph.d. thesis where these results were originally proved and suggested several improvements to a previous version of this paper. I wish also to thank MAURICE POUZET, who explained to me his theorem which is an important tool in the proof of the main result of this paper, and ALESSANDRO ANDRETTA, whose interest in this result stimulated the writing of this paper"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universita\u0301 di Torino Via Carlo Alberto 10, I\u201310123 Torino, Italy","institution_ids":["https://openalex.org/I1330701686"]},{"raw_affiliation_string":"I am very much indebted to STEPHEN G. SIMPSON, who introduced me to bqo theory, supervised my Ph.d. thesis where these results were originally proved and suggested several improvements to a previous version of this paper. I wish also to thank MAURICE POUZET, who explained to me his theorem which is an important tool in the proof of the main result of this paper, and ALESSANDRO ANDRETTA, whose interest in this result stimulated the writing of this paper","institution_ids":["https://openalex.org/I4210111890"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047796693"],"corresponding_institution_ids":["https://openalex.org/I1330701686","https://openalex.org/I4210111890"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":1.0713,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.73985412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"41","issue":"3","first_page":"373","last_page":"383"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9979000091552734,"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":0.897101640701294},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.8841570615768433},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.7672187089920044},{"id":"https://openalex.org/keywords/cantor-set","display_name":"Cantor set","score":0.5832830667495728},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5547451376914978},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.5127428770065308},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5089583396911621},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49240005016326904},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4036279320716858},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32265710830688477},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06486576795578003},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06101757287979126}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.897101640701294},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8841570615768433},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.7672187089920044},{"id":"https://openalex.org/C36605576","wikidata":"https://www.wikidata.org/wiki/Q273188","display_name":"Cantor set","level":2,"score":0.5832830667495728},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5547451376914978},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.5127428770065308},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5089583396911621},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49240005016326904},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4036279320716858},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32265710830688477},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06486576795578003},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06101757287979126},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.19950410309","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19950410309","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"},{"id":"pmh:oai:air.uniud.it:11390/675417","is_oa":false,"landing_page_url":"http://hdl.handle.net/11390/675417","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W286191049","https://openalex.org/W296433066","https://openalex.org/W586883305","https://openalex.org/W1530843743","https://openalex.org/W1555991696","https://openalex.org/W2082065673","https://openalex.org/W2138899395","https://openalex.org/W2163841074","https://openalex.org/W2218992691","https://openalex.org/W2316932045","https://openalex.org/W4206193192","https://openalex.org/W4211074246","https://openalex.org/W4236220564","https://openalex.org/W4239860664","https://openalex.org/W6650008539"],"related_works":["https://openalex.org/W4289754218","https://openalex.org/W4382795714","https://openalex.org/W4386399178","https://openalex.org/W2863395758","https://openalex.org/W3094338803","https://openalex.org/W3139954723","https://openalex.org/W4375858716","https://openalex.org/W3009259455","https://openalex.org/W2113622161","https://openalex.org/W4297571715"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4,52],"give":[5],"a":[6,24],"proof":[7],"of":[8,14,17,26,58],"the":[9,15,27,41],"II":[10],"1":[11],"2":[12],"\u2010completeness":[13],"set":[16],"countable":[18],"better":[19,59],"quasi":[20,60],"orderings":[21],"(viewed":[22],"as":[23,64,68],"subset":[25],"Cantor":[28],"space).":[29],"This":[30],"result":[31],"was":[32],"conjectured":[33],"by":[34,40],"Clote":[35],"in":[36,43],"[2]":[37],"and":[38,63],"proved":[39],"author":[42],"his":[44],"Ph.d.":[45],"thesis":[46],"[6]":[47],"(see":[48],"also":[49],"[7]).":[50],"Here":[51],"prove":[53],"it":[54],"using":[55],"Simpson's":[56],"definition":[57],"ordering":[61],"([15])":[62],"little":[65],"bqo":[66],"theory":[67],"possible.":[69]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}