{"id":"https://openalex.org/W2080750825","doi":"https://doi.org/10.2178/jsl/1082418539","title":"Combinatorics for the dominating and unsplitting numbers","display_name":"Combinatorics for the dominating and unsplitting numbers","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W2080750825","doi":"https://doi.org/10.2178/jsl/1082418539","mag":"2080750825"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1082418539","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1082418539","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic 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/A5112323292","display_name":"Jason Aaron Aubrey","orcid":null},"institutions":[{"id":"https://openalex.org/I119234918","display_name":"University of Northern Iowa","ror":"https://ror.org/02h4qpx12","country_code":"US","type":"education","lineage":["https://openalex.org/I119234918"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jason Aubrey","raw_affiliation_strings":["Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506, USA, E-mail:","[University of Northern Iowa]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506, USA, E-mail:","institution_ids":["https://openalex.org/I119234918"]},{"raw_affiliation_string":"[University of Northern Iowa]","institution_ids":["https://openalex.org/I119234918"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112323292"],"corresponding_institution_ids":["https://openalex.org/I119234918"],"apc_list":null,"apc_paid":null,"fwci":0.7858,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.70372836,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"69","issue":"2","first_page":"482","last_page":"498"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.8497480154037476},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6906927227973938},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.667171835899353},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5527009963989258},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49310538172721863},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4435714781284332},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4271332621574402},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.1712404489517212},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09428662061691284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8497480154037476},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6906927227973938},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.667171835899353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5527009963989258},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49310538172721863},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4435714781284332},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4271332621574402},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.1712404489517212},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09428662061691284},{"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/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/jsl/1082418539","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1082418539","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:scholarworks.uni.edu:facpub-4105","is_oa":false,"landing_page_url":"https://scholarworks.uni.edu/facpub/3104","pdf_url":null,"source":{"id":"https://openalex.org/S4377196489","display_name":"UNI ScholarWorks (University of Northern Iowa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119234918","host_organization_name":"University of Northern Iowa","host_organization_lineage":["https://openalex.org/I119234918"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1082418539","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1082418539","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W866141558","https://openalex.org/W872818295","https://openalex.org/W1967718874","https://openalex.org/W1985615626","https://openalex.org/W2032346220","https://openalex.org/W2049313173","https://openalex.org/W2091592436","https://openalex.org/W2122611567","https://openalex.org/W2170688910","https://openalex.org/W3176068709","https://openalex.org/W4238357114","https://openalex.org/W6797234261"],"related_works":["https://openalex.org/W2002177687","https://openalex.org/W2058438338","https://openalex.org/W2019471580","https://openalex.org/W3184131894","https://openalex.org/W2941284322","https://openalex.org/W4224920876","https://openalex.org/W2168299207","https://openalex.org/W3018679651","https://openalex.org/W24519920","https://openalex.org/W2087778462"],"abstract_inverted_index":{"Abstract.":[0],"In":[1],"this":[2],"paper":[3],"we":[4],"introduce":[5],"a":[6,42,79],"new":[7],"property":[8],"of":[9,11,23,29,32,41,91,108,124],"families":[10,25],"functions":[12,109,125],"on":[13],"the":[14,21,27,33,38,56,92,114],"Baire":[15],"space,":[16],"called":[17],"pseudo-dominating,":[18,111],"and":[19,64,112],"apply":[20],"properties":[22],"these":[24],"to":[26,120],"study":[28],"cardinal":[30],"characteristics":[31],"continuum.":[34],"We":[35,51,75,96],"show":[36,76,98],"that":[37,77,86,99,104,113],"minimum":[39],"cardinality":[40],"pseudo-dominating":[43],"family":[44,81,107,123],"is":[45,82,94,110,118],"min":[46],"{":[47],"\u03c4,":[48],"\u2202":[49],"}.":[50,74],"derive":[52],"two":[53],"corollaries":[54],"from":[55],"proof:":[57],"\u03c4":[58,67,72],"\u2265":[59],"min{":[60,65,70],"\u2202,":[61,66,71],"u":[62,100],"}":[63,68],"=":[69],"\u03c3":[73],"if":[78],"dominating":[80],"partitioned":[83],"into":[84],"fewer":[85],"s":[87],"pieces,":[88],"then":[89],"one":[90],"pieces":[93],"pseudo-dominating.":[95,128],"finally":[97],"&lt;":[101],"g":[102],"implies":[103],"every":[105,121],"unbounded":[106,122],"Filter":[115],"Dichotomy":[116],"principle":[117],"equivalent":[119],"being":[126],"finitely":[127]},"counts_by_year":[{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
