{"id":"https://openalex.org/W1965382255","doi":"https://doi.org/10.1002/malq.200410047","title":"Generalized Prikry forcing and iteration of generic ultrapowers","display_name":"Generalized Prikry forcing and iteration of generic ultrapowers","publication_year":2005,"publication_date":"2005-08-03","ids":{"openalex":"https://openalex.org/W1965382255","doi":"https://doi.org/10.1002/malq.200410047","mag":"1965382255"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200410047","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410047","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5101748746","display_name":"Hiroshi Sakai","orcid":"https://orcid.org/0000-0003-2116-8657"},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hiroshi Sakai","raw_affiliation_strings":["Graduate School of Human Informatics, Nagoya University, Furocho, Chikusaku, Nagoya 464 \u2013 8601, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Human Informatics, Nagoya University, Furocho, Chikusaku, Nagoya 464 \u2013 8601, Japan","institution_ids":["https://openalex.org/I60134161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101748746"],"corresponding_institution_ids":["https://openalex.org/I60134161"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07191192,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"5","first_page":"507","last_page":"523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":1.0,"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":1.0,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9962999820709229,"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/forcing","display_name":"Forcing (mathematics)","score":0.7458778619766235},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7361640930175781},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6980478763580322},{"id":"https://openalex.org/keywords/ultrafilter","display_name":"Ultrafilter","score":0.5445308089256287},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4124095141887665},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3848457932472229},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32151657342910767},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16145512461662292},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1209595799446106},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.04280954599380493}],"concepts":[{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.7458778619766235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7361640930175781},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6980478763580322},{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.5445308089256287},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4124095141887665},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3848457932472229},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32151657342910767},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16145512461662292},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1209595799446106},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.04280954599380493},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200410047","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410047","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"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/W373642563","https://openalex.org/W656854703","https://openalex.org/W1536273738","https://openalex.org/W1595388840","https://openalex.org/W2060319527","https://openalex.org/W2061591255","https://openalex.org/W2073618502","https://openalex.org/W2082862920","https://openalex.org/W2117873821","https://openalex.org/W2478289388","https://openalex.org/W6612675781","https://openalex.org/W6621949684"],"related_works":["https://openalex.org/W1931954019","https://openalex.org/W2905066517","https://openalex.org/W4385781459","https://openalex.org/W4286971162","https://openalex.org/W3200176881","https://openalex.org/W3015674040","https://openalex.org/W4288418747","https://openalex.org/W2513337872","https://openalex.org/W3210303987","https://openalex.org/W4210813124"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,6,20,43,71],"known":[3],"that":[4],"there":[5],"a":[7,21,25,72],"close":[8],"relation":[9],"between":[10],"Prikry":[11,73],"forcing":[12],"and":[13,29],"the":[14,44,54],"iteration":[15,45],"of":[16,46,48,56],"ultrapowers:":[17],"If":[18],"U":[19,51],"normal":[22,87],"ultrafilter":[23],"on":[24],"measurable":[26],"cardinal":[27],"\u03ba":[28,64],"\u3008":[30,59],"M":[31,77],"n":[32,39,62,67],",":[33,52],"j":[34,60],"m,n":[35],"|":[36,66],"m":[37],"\u2264":[38,40],"\u03c9":[41,69,78],"\u3009":[42,70],"ultrapowers":[47],"V":[49],"by":[50],"then":[53],"sequence":[55,75],"critical":[57],"points":[58],"0,":[61],"(":[63],")":[65],"\u2208":[68],"generic":[74],"over":[76],".":[79],"In":[80],"this":[81,85],"paper":[82],"we":[83],"generalize":[84],"for":[86],"precipitous":[88],"filters.":[89],"(\u00a9":[90],"2005":[91],"WILEY\u2010VCH":[92],"Verlag":[93],"GmbH":[94],"&amp;":[95],"Co.":[96],"KGaA,":[97],"Weinheim)":[98]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
