{"id":"https://openalex.org/W2017892908","doi":"https://doi.org/10.1016/0168-0072(86)90067-9","title":"Members of countable \u03c010 classes","display_name":"Members of countable \u03c010 classes","publication_year":1986,"publication_date":"1986-01-01","ids":{"openalex":"https://openalex.org/W2017892908","doi":"https://doi.org/10.1016/0168-0072(86)90067-9","mag":"2017892908"},"language":"en","primary_location":{"id":"doi:10.1016/0168-0072(86)90067-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(86)90067-9","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/A5057979748","display_name":"Douglas Cenzer","orcid":"https://orcid.org/0000-0002-6029-9900"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Douglas Cenzer","raw_affiliation_strings":["Dept. of Mathematics, University of Florida, Gainesville, FL 32611, USA","Department of Mathematics, University of  Florida, Gainesville, FL 32611, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mathematics, University of  Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038186958","display_name":"Peter Clote","orcid":"https://orcid.org/0000-0003-3628-2874"},"institutions":[{"id":"https://openalex.org/I103531236","display_name":"Boston College","ror":"https://ror.org/02n2fzt79","country_code":"US","type":"education","lineage":["https://openalex.org/I103531236"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Clote","raw_affiliation_strings":["Boston College, Chestnut Hill, MA 02167, USA","Boston College, Chestnut Hill, MA, 02167, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston College, Chestnut Hill, MA 02167, USA","institution_ids":["https://openalex.org/I103531236"]},{"raw_affiliation_string":"Boston College, Chestnut Hill, MA, 02167, USA","institution_ids":["https://openalex.org/I103531236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073925948","display_name":"Rick L. Smith","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rick L. Smith","raw_affiliation_strings":["Dept. of Mathematics, University of Florida, Gainesville, FL 32611, USA","Department of Mathematics, University of  Florida, Gainesville, FL 32611, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mathematics, University of  Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023422267","display_name":"Robert I. Soare","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert I. Soare","raw_affiliation_strings":["University of Chicago, Chicago, IL 60637, USA","University of Chicago, Chicago, IL 60637 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chicago, Chicago, IL 60637, USA","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"University of Chicago, Chicago, IL 60637 USA","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113891766","display_name":"Stanley S. Wainer","orcid":null},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stanley S. Wainer","raw_affiliation_strings":["University of Leeds, Leeds, LS2 9JT, UK","University of Leeds, Leeds LS2 9JT, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Leeds, Leeds, LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"University of Leeds, Leeds LS2 9JT, UK#TAB#","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":2.7734,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.89314079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":null,"first_page":"145","last_page":"163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.994700014591217,"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"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.994700014591217,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9912999868392944,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9542999863624573,"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/countable-set","display_name":"Countable set","score":0.8237996101379395},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7586155533790588},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4339454174041748},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39594775438308716},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33794867992401123},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1583862602710724},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13266196846961975}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8237996101379395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7586155533790588},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4339454174041748},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39594775438308716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33794867992401123},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1583862602710724},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13266196846961975}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0168-0072(86)90067-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(86)90067-9","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W83139932","https://openalex.org/W1554860413","https://openalex.org/W1963765293","https://openalex.org/W2007915800","https://openalex.org/W2038972143","https://openalex.org/W2083623332","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W4234930915","https://openalex.org/W6641145293"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1631776469","https://openalex.org/W2541640833","https://openalex.org/W4206367340"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}