{"id":"https://openalex.org/W2127047043","doi":"https://doi.org/10.2178/jsl/1080938830","title":"Analytic countably splitting families","display_name":"Analytic countably splitting families","publication_year":2004,"publication_date":"2004-03-01","ids":{"openalex":"https://openalex.org/W2127047043","doi":"https://doi.org/10.2178/jsl/1080938830","mag":"2127047043"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1080938830","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1080938830","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/A5053840680","display_name":"Otmar Spinas","orcid":null},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Christian-Albrechts-Universit\u00e4t zu Kiel","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Otmar Spinas","raw_affiliation_strings":["Mathematisches Seminar, Christian-Albrechts-Universit\u00e4t Zu Kiel, Ludewig-Meyn-Stra\u00dfe 4, 24098 Kiel, Germany, E-mail:","Christian-Albrechts-Universit\u00c4t zu Kiel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Seminar, Christian-Albrechts-Universit\u00e4t Zu Kiel, Ludewig-Meyn-Stra\u00dfe 4, 24098 Kiel, Germany, E-mail:","institution_ids":["https://openalex.org/I32021983"]},{"raw_affiliation_string":"Christian-Albrechts-Universit\u00c4t zu Kiel","institution_ids":["https://openalex.org/I32021983"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053840680"],"corresponding_institution_ids":["https://openalex.org/I32021983"],"apc_list":null,"apc_paid":null,"fwci":1.2576,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.78728433,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"69","issue":"1","first_page":"101","last_page":"117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9876000285148621,"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/T12137","display_name":"Economic theories and models","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.9496894478797913},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6471987366676331},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3927878141403198},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33246996998786926},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32381075620651245}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.9496894478797913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6471987366676331},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3927878141403198},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33246996998786926},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32381075620651245}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/jsl/1080938830","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1080938830","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:CULeuclid:euclid.jsl/1080938830","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1080938830","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.5678","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.5678","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-computerlabor.math.uni-kiel.de/~spinas/engl/SplitFam.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W148883224","https://openalex.org/W1539382740","https://openalex.org/W1846481405","https://openalex.org/W1964181935","https://openalex.org/W1978413491","https://openalex.org/W1993721769","https://openalex.org/W2038277696","https://openalex.org/W2099895731","https://openalex.org/W2101606222","https://openalex.org/W2506650614","https://openalex.org/W4234853174","https://openalex.org/W4248784701","https://openalex.org/W6725085109"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2950866767","https://openalex.org/W2142036596","https://openalex.org/W2541640833","https://openalex.org/W4206367340","https://openalex.org/W1606946808"],"abstract_inverted_index":{"Abstract":[0],"A":[1,3,26],"family":[2,52,82],"\u2286":[4,17],"(":[5],"\u03c9":[6,19,21],")":[7],"is":[8],"called":[9],"countably":[10,50,56],"splitting":[11,39,51,57,81,89],"if":[12],"for":[13],"every":[14,28,48],"countable":[15],"F":[16,31,79],"[":[18],"]":[20],",":[22],"some":[23],"element":[24],"of":[25,30,37,43,61,67],"splits":[27],"member":[29],".":[32],"We":[33],"define":[34],"a":[35,38,54,65,87],"notion":[36,63],"tree,":[40],"by":[41],"means":[42],"which":[44],"we":[45,73],"prove":[46],"that":[47,75,83],"analytic":[49],"contains":[53],"closed":[55,88],"family.":[58,90],"An":[59],"application":[60],"this":[62],"solves":[64],"problem":[66],"Blass.":[68],"On":[69],"the":[70],"other":[71],"hand":[72],"show":[74],"there":[76],"exists":[77],"an":[78],"\u03c3":[80],"does":[84],"not":[85],"contain":[86]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}