{"id":"https://openalex.org/W2042716103","doi":"https://doi.org/10.1002/malq.201020081","title":"Ideals with bases of unbounded Borel complexity","display_name":"Ideals with bases of unbounded Borel complexity","publication_year":2011,"publication_date":"2011-08-02","ids":{"openalex":"https://openalex.org/W2042716103","doi":"https://doi.org/10.1002/malq.201020081","mag":"2042716103"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201020081","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201020081","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/A5047648974","display_name":"Piotr Borodulin\u2013Nadzieja","orcid":"https://orcid.org/0000-0002-2208-6381"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Borodulin-Nadzieja","raw_affiliation_strings":["Instytut Matematyczny, Uniwersytet Wroc\u0142awski, pl. Grunwaldzki 2/4, 50-384 Wroc\u0142aw, Poland","Instytut Matematyczny, Uniwersytet Wroc\u0142awski, pl. Grunwaldzki 2/4, 50\u2010384, Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instytut Matematyczny, Uniwersytet Wroc\u0142awski, pl. Grunwaldzki 2/4, 50-384 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]},{"raw_affiliation_string":"Instytut Matematyczny, Uniwersytet Wroc\u0142awski, pl. Grunwaldzki 2/4, 50\u2010384, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085489153","display_name":"Szymon G\u0142a\u0327b","orcid":"https://orcid.org/0000-0001-9026-8235"},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Szymon G\u0142a\u0327b","raw_affiliation_strings":["Institute of Mathematics, Technical University of \u0141o\u0301dz\u0301, ul. Wo\u0301lczan\u0301ska 215, 90-924 \u0141o\u0301dz\u0301, Poland","Institute of Mathematics, Technical University of \u0141\u00f3d\u017a, ul. W\u00f3lcza\u0144ska 215, 90\u2010924 \u0141\u00f3d\u017a, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technical University of \u0141o\u0301dz\u0301, ul. Wo\u0301lczan\u0301ska 215, 90-924 \u0141o\u0301dz\u0301, Poland","institution_ids":["https://openalex.org/I188884621","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Institute of Mathematics, Technical University of \u0141\u00f3d\u017a, ul. W\u00f3lcza\u0144ska 215, 90\u2010924 \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I188884621","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":1.0562,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7493399,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"57","issue":"6","first_page":"582","last_page":"590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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":0.9962999820709229,"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":0.9147968292236328},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6724497079849243},{"id":"https://openalex.org/keywords/borel-set","display_name":"Borel set","score":0.6385658979415894},{"id":"https://openalex.org/keywords/borel-hierarchy","display_name":"Borel hierarchy","score":0.5727150440216064},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48405852913856506},{"id":"https://openalex.org/keywords/borel-equivalence-relation","display_name":"Borel equivalence relation","score":0.4776395857334137},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4661005735397339},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38141465187072754},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.34097129106521606},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07599309086799622},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.055510491132736206},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.033354610204696655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9147968292236328},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6724497079849243},{"id":"https://openalex.org/C39952206","wikidata":"https://www.wikidata.org/wiki/Q21086747","display_name":"Borel set","level":2,"score":0.6385658979415894},{"id":"https://openalex.org/C25942563","wikidata":"https://www.wikidata.org/wiki/Q893487","display_name":"Borel hierarchy","level":4,"score":0.5727150440216064},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48405852913856506},{"id":"https://openalex.org/C5278979","wikidata":"https://www.wikidata.org/wiki/Q4944905","display_name":"Borel equivalence relation","level":4,"score":0.4776395857334137},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4661005735397339},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38141465187072754},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.34097129106521606},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07599309086799622},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.055510491132736206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.033354610204696655},{"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.201020081","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201020081","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1539382740","https://openalex.org/W1544272473","https://openalex.org/W1966168973","https://openalex.org/W1983120318","https://openalex.org/W1987380049","https://openalex.org/W1995217618","https://openalex.org/W2007083429","https://openalex.org/W2037769602","https://openalex.org/W2043667610","https://openalex.org/W2109373871","https://openalex.org/W2121739804","https://openalex.org/W2123346811","https://openalex.org/W2157774627","https://openalex.org/W4210359368"],"related_works":["https://openalex.org/W1491956444","https://openalex.org/W2063281146","https://openalex.org/W2031042539","https://openalex.org/W2080776953","https://openalex.org/W4243177823","https://openalex.org/W1977210292","https://openalex.org/W2964069349","https://openalex.org/W4299887575","https://openalex.org/W2201015916","https://openalex.org/W839722575"],"abstract_inverted_index":{"We":[0,24],"present":[1],"several":[2],"naturally":[3],"defined":[4],"\u03c3-ideals":[5],"which":[6],"have":[7],"Borel":[8,22],"bases":[9],"but,":[10],"unlike":[11],"for":[12],"the":[13],"classical":[14],"examples,":[15],"these":[16],"ideals":[17],"are":[18],"not":[19],"of":[20,28],"bounded":[21],"complexity.":[23],"investigate":[25],"set-theoretic":[26],"properties":[27],"such":[29],"\u03c3-ideals.":[30]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}