{"id":"https://openalex.org/W3006395458","doi":"https://doi.org/10.1215/00294527-2020-0002","title":"A Note on Strongly Almost Disjoint Families","display_name":"A Note on Strongly Almost Disjoint Families","publication_year":2020,"publication_date":"2020-02-14","ids":{"openalex":"https://openalex.org/W3006395458","doi":"https://doi.org/10.1215/00294527-2020-0002","mag":"3006395458"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2020-0002","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-2020-0002","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal 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/A5069470371","display_name":"Guozhen Shen","orcid":"https://orcid.org/0000-0003-0100-2318"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guozhen Shen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069470371"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5454,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5643915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"61","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9362000226974487,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9362000226974487,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.9448635578155518},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.8149412870407104},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.781927227973938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7464439868927002},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.7168005108833313},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4711141884326935},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4649433195590973},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.446278840303421},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41588151454925537},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.2945414185523987},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08318755030632019},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0431922972202301}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.9448635578155518},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8149412870407104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.781927227973938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7464439868927002},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.7168005108833313},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4711141884326935},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4649433195590973},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.446278840303421},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41588151454925537},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2945414185523987},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08318755030632019},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0431922972202301},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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:10.1215/00294527-2020-0002","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-2020-0002","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1581649448","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1581649448","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1997237005","https://openalex.org/W2126219331","https://openalex.org/W2161061660","https://openalex.org/W2771826017","https://openalex.org/W4230632233"],"related_works":["https://openalex.org/W132109778","https://openalex.org/W1989984537","https://openalex.org/W2499670206","https://openalex.org/W2901423989","https://openalex.org/W2087878692","https://openalex.org/W4283312226","https://openalex.org/W2012063272","https://openalex.org/W1974981985","https://openalex.org/W2096720787","https://openalex.org/W2052907214"],"abstract_inverted_index":{"For":[0],"a":[1],"set":[2,75],"M,":[3],"let":[4],"|M|":[5],"denote":[6],"the":[7,42,73],"cardinality":[8],"of":[9,34,44,76],"M.":[10,77],"A":[11],"family":[12],"F":[13],"is":[14,21,37],"called":[15],"strongly":[16,54],"almost":[17,55],"disjoint":[18,56],"if":[19],"there":[20,61],"an":[22],"n\u2208\u03c9":[23],"such":[24],"that":[25],"|A\u2229B|<n":[26],"for":[27,47],"any":[28],"two":[29],"distinct":[30],"elements":[31],"A,":[32],"B":[33],"F.":[35],"It":[36],"shown":[38],"in":[39],"ZF":[40],"(without":[41],"axiom":[43],"choice)":[45],"that,":[46],"all":[48,53],"infinite":[49],"sets":[50],"M":[51],"and":[52,60],"families":[57],"F\u2286P(M),":[58],"|F|<|P(M)|":[59],"are":[62],"no":[63],"finite-to-one":[64],"functions":[65],"from":[66],"P(M)":[67,71],"into":[68],"F,":[69],"where":[70],"denotes":[72],"power":[74]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}