{"id":"https://openalex.org/W1550331046","doi":"https://doi.org/10.2307/2275289","title":"Adding dominating reals with <i>\u03c9</i><sup><i>\u03c9</i></sup> of bounding posets","display_name":"Adding dominating reals with <i>\u03c9</i><sup><i>\u03c9</i></sup> of bounding posets","publication_year":1992,"publication_date":"1992-06-01","ids":{"openalex":"https://openalex.org/W1550331046","doi":"https://doi.org/10.2307/2275289","mag":"1550331046"},"language":"en","primary_location":{"id":"doi:10.2307/2275289","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275289","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/A5086050031","display_name":"Janusz Pawlikowski","orcid":"https://orcid.org/0000-0003-2022-6608"},"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":true,"raw_author_name":"Janusz Pawlikowski","raw_affiliation_strings":["Instytut Matematyczny, Uniwersytet Wrog\u0142awski, 50-384 Wroc\u0142aw, Poland","Uniwersytet Wrog\u0142awski"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instytut Matematyczny, Uniwersytet Wrog\u0142awski, 50-384 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]},{"raw_affiliation_string":"Uniwersytet Wrog\u0142awski","institution_ids":["https://openalex.org/I219388962"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086050031"],"corresponding_institution_ids":["https://openalex.org/I219388962"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.06393862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"57","issue":"2","first_page":"540","last_page":"547"},"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":0.9873999953269958,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9842000007629395,"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/forcing","display_name":"Forcing (mathematics)","score":0.8626978397369385},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.6767661571502686},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6052548289299011},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5126318335533142},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4772458076477051},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4283480644226074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29173874855041504},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07701516151428223},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06791931390762329},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0498204231262207}],"concepts":[{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.8626978397369385},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6767661571502686},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6052548289299011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5126318335533142},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4772458076477051},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4283480644226074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29173874855041504},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07701516151428223},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06791931390762329},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0498204231262207}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2275289","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275289","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1984454806","https://openalex.org/W2029749844","https://openalex.org/W4211074246","https://openalex.org/W4243208804"],"related_works":["https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2971214053","https://openalex.org/W2369178846","https://openalex.org/W2082716031","https://openalex.org/W2370289839","https://openalex.org/W2933494595","https://openalex.org/W2949231297","https://openalex.org/W2060606417","https://openalex.org/W1568049691"],"abstract_inverted_index":{"Let":[0],"B":[1,22,60,99,133,170],"be":[2,101],"the":[3,69,88,107,116,151,155,168,186,201],"random":[4],"real":[5,73,80,110,142,178,198],"forcing.":[6],"Miller":[7,206],"[Mi]":[8,207],"asked":[9],"if":[10],"there":[11],"are":[12],"ZFC":[13],"models":[14],"M":[15,23],"\u2286":[16],"N":[17,25],"such":[18,50],"that":[19,57,98,125,160,209],"forcing":[20,58,74,111,161,199],"with":[21,59,165],"over":[24,62,81,143,162,179],"adds":[26,77,175],"a":[27,43,78,139,176],"dominating":[28,79,141,177],"real.":[29],"A":[30],"YES":[31,89],"answer":[32,90],"was":[33],"provided":[34],"by":[35,104,128,204],"Judah":[36],"and":[37,45,134,190],"Shelah":[38],"in":[39,42],"[JS],":[40],"where":[41,66],"long":[44],"sophisticated":[46],"construction":[47],"they":[48],"built":[49],"models.":[51],"In":[52,146],"this":[53,147],"paper":[54],"we":[55,149,158,184],"prove":[56,124,159],"V":[61,63,82,144,163,171,174,180],"I":[64,67,83,131,135,164,181,189,210],",":[65,106],"is":[68,200,211],"infinitely":[70,195],"often":[71,196],"equal":[72,197],"of":[75,112,119,154,167,188],"[Mi],":[76],".":[84,145,182],"This":[85,114],"greatly":[86],"simplifies":[87],"to":[91],"Miller's":[92,120],"question.":[93,121],"Moreover":[94],"it":[95],"turns":[96],"out":[97],"may":[100],"replaced":[102],"here":[103],"E":[105,137,173,191],"eventually":[108],"different":[109],"[Mi].":[113,193],"answers":[115],"second":[117],"part":[118],"We":[122],"also":[123],"both":[126],"side":[127,129],"products":[130],"\u00d7":[132,136],"add":[138],"Hechler":[140],"section":[148],"establish":[150],"main":[152],"result":[153],"paper;":[156],"namely,":[157],"either":[166],"posets":[169],"or":[172],"First":[183],"recall":[185],"definitions":[187],"from":[192],"The":[194],"set":[202],"ordered":[203],"extension.":[205],"proves":[208],"\u03c9":[212,213],"bounding.":[214]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}