{"id":"https://openalex.org/W2087042737","doi":"https://doi.org/10.2178/jsl/1190150156","title":"On regular reduced products","display_name":"On regular reduced products","publication_year":2002,"publication_date":"2002-09-01","ids":{"openalex":"https://openalex.org/W2087042737","doi":"https://doi.org/10.2178/jsl/1190150156","mag":"2087042737"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150156","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150156","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/A5021752135","display_name":"Juliette Kennedy","orcid":"https://orcid.org/0000-0001-6567-4098"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Juliette Kennedy","raw_affiliation_strings":["Department of Mathematics, University of Helsinki, Helsinki, Finland, E-mail:","Department of Mathematics, University of Helsinki, Helsinki, Finland, E-mail: juliette.kennedy@helsinki.fi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Helsinki, Helsinki, Finland, E-mail:","institution_ids":["https://openalex.org/I133731052"]},{"raw_affiliation_string":"Department of Mathematics, University of Helsinki, Helsinki, Finland, E-mail: juliette.kennedy@helsinki.fi","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024923217","display_name":"Saharon Shelah","orcid":"https://orcid.org/0000-0003-0462-3152"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Saharon Shelah","raw_affiliation_strings":["Institute of Mathematics, Hebrew University, Jerusalem, Israel, E-mail:","Institute of Mathematics, Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hebrew University, Jerusalem, Israel, E-mail:","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"Institute of Mathematics, Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.3943,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79568832,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"67","issue":"3","first_page":"1169","last_page":"1177"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9833999872207642,"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":0.9717000126838684,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.819787859916687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8137905597686768},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6907952427864075},{"id":"https://openalex.org/keywords/ultrafilter","display_name":"Ultrafilter","score":0.665634274482727},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6403422355651855},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6040657162666321},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.5219640135765076},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4834514558315277},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.45350244641304016},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06820759177207947}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.819787859916687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8137905597686768},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6907952427864075},{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.665634274482727},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6403422355651855},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6040657162666321},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.5219640135765076},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4834514558315277},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.45350244641304016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06820759177207947},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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":2,"locations":[{"id":"doi:10.2178/jsl/1190150156","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150156","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/1190150156","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150156","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1976092383","https://openalex.org/W1978905809","https://openalex.org/W2005659848","https://openalex.org/W2026593029","https://openalex.org/W2036951624","https://openalex.org/W2040139506","https://openalex.org/W2056201127","https://openalex.org/W2070476230","https://openalex.org/W2122092051","https://openalex.org/W2724270706","https://openalex.org/W2799061192"],"related_works":["https://openalex.org/W2331093826","https://openalex.org/W2147918975","https://openalex.org/W2171296020","https://openalex.org/W2957668530","https://openalex.org/W2991932127","https://openalex.org/W2023451621","https://openalex.org/W2515805800","https://openalex.org/W2809776903","https://openalex.org/W2058921901","https://openalex.org/W2288701235"],"abstract_inverted_index":{"Abstract":[0],"Assume":[1,7,167],"(\u21350,":[2,134,174],"\u21351)":[3,135,175],"\u2192":[4,136,176],"(\u03bb,":[5,137,177],"\u03bb+).":[6],"M":[8,59,74,86],"is":[9,60,75,97,102,127,193],"a":[10,13,24,33,42,53,91,118,128,148,194],"model":[11,34],"of":[12,18,26,44,117,155],"first":[14,45],"order":[15,46],"theory":[16],"T":[17],"cardinality":[19,27,122],"at":[20],"most":[21],"\u03bb+":[22,157],"in":[23,48,73,78,151],"language":[25,119],"\u2264":[28,123],"\u03bb.":[29,57,124],"Let":[30,39],"N":[31],"be":[32,41,52,113,188],"with":[35],"the":[36,63,82,144,152,164],"same":[37],"language.":[38],"\u0394":[40],"set":[43],"formulas":[47],"and":[49,89,111,133,160,169,179,186],"let":[50,109],"D":[51,90,126,192],"regular":[54,92,129,171,195],"filter":[55,130,196],"on":[56,131,158,197],"Then":[58],"\u0394-embeddable":[61],"into":[62],"reduced":[64],"power":[65],"N\u03bb/D,":[66],"provided":[67],"that":[68,142],"every":[69],"\u0394-existential":[70],"formula":[71],"true":[72,76],"also":[77],"N.":[79],"We":[80,140],"obtain":[81],"following":[83,165],"corollary:":[84,166],"for":[85],"as":[87,103,189],"above":[88],"ultrafilter":[93],"over":[94],"\u03bb,":[95,198],"M\u03bb/D":[96],"\u03bb++-universal.":[98],"Our":[99],"second":[100,145],"result":[101],"follows:":[104],"For":[105,183],"i":[106],"<":[107],"\u03bc":[108],"Mi,":[110],"Ni,":[112],"elementarily":[114],"equivalent":[115],"models":[116],"which":[120],"has":[121,147],"Suppose":[125],"\u03bb":[132,170],"\u03bb+)":[138,178],"holds.":[139],"show":[141],"then":[143,199],"player":[146],"winning":[149],"strategy":[150],"Ehrenfeucht-Fra\u00efss\u00e9":[153],"game":[154],"length":[156],"\u03a0iMi/D":[159,200],"\u03a0iNi/D.":[161,202],"This":[162],"yields":[163],"GCH":[168],"(or":[172],"just":[173],"2\u03bb":[180],"=":[181],"\u03bb+.":[182],"L,":[184],"Mi":[185],"Ni":[187],"above,":[190],"if":[191],"\u2245":[201]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}