{"id":"https://openalex.org/W2014240393","doi":"https://doi.org/10.2178/jsl/1286198153","title":"Diagonal Prikry extensions","display_name":"Diagonal Prikry extensions","publication_year":2010,"publication_date":"2010-10-04","ids":{"openalex":"https://openalex.org/W2014240393","doi":"https://doi.org/10.2178/jsl/1286198153","mag":"2014240393"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1286198153","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1286198153","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Diagonal_Prikry_extensions/6477221","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081789569","display_name":"James Cummings","orcid":"https://orcid.org/0000-0002-7913-0427"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Cummings","raw_affiliation_strings":["Mathematical Sciences Department, Carnegie Mellon University, Pittsburgh PA 15215, USA. E-mail:","Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Department, Carnegie Mellon University, Pittsburgh PA 15215, USA. E-mail:","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110862887","display_name":"Matthew Foreman","orcid":null},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]},{"id":"https://openalex.org/I2803209242","display_name":"University of California System","ror":"https://ror.org/00pjdza24","country_code":"US","type":"education","lineage":["https://openalex.org/I2803209242"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew Foreman","raw_affiliation_strings":["Department of Mathematics, University of California, Irvine, Irvine CA 92697, USA. E-mail:","University of California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine, Irvine CA 92697, USA. E-mail:","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"University of California","institution_ids":["https://openalex.org/I2803209242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1315,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.86427034,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"75","issue":"4","first_page":"1383","last_page":"1402"},"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":0.9901000261306763,"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":0.9833999872207642,"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/uncountable-set","display_name":"Uncountable set","score":0.8431978225708008},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7650055885314941},{"id":"https://openalex.org/keywords/regular-cardinal","display_name":"Regular cardinal","score":0.7491751909255981},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6806352734565735},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6682198643684387},{"id":"https://openalex.org/keywords/successor-cardinal","display_name":"Successor cardinal","score":0.5219035744667053},{"id":"https://openalex.org/keywords/core-model","display_name":"Core model","score":0.44954273104667664},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.44015222787857056},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4349229633808136},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43419161438941956},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.2702943682670593},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08160340785980225},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08109584450721741}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.8431978225708008},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7650055885314941},{"id":"https://openalex.org/C89507440","wikidata":"https://www.wikidata.org/wiki/Q1193137","display_name":"Regular cardinal","level":2,"score":0.7491751909255981},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6806352734565735},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6682198643684387},{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.5219035744667053},{"id":"https://openalex.org/C2780366209","wikidata":"https://www.wikidata.org/wiki/Q5170200","display_name":"Core model","level":2,"score":0.44954273104667664},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.44015222787857056},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4349229633808136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43419161438941956},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.2702943682670593},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08160340785980225},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08109584450721741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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":7,"locations":[{"id":"doi:10.2178/jsl/1286198153","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1286198153","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.225.4909","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.225.4909","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/users/jcumming/papers/newprikry_2009_final_revised.pdf","raw_type":"text"},{"id":"pmh:oai:repository.cmu.edu:math-1734","is_oa":false,"landing_page_url":"http://repository.cmu.edu/math/723","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Mathematical Sciences","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6477221","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal contribution"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1286198153","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1286198153","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:figshare.com:article/6477221","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Diagonal_Prikry_extensions/6477221","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.1184/r1/6477221.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6477221.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/6477221","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Diagonal_Prikry_extensions/6477221","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W779054633","https://openalex.org/W1582291305","https://openalex.org/W1869154077","https://openalex.org/W1963677918","https://openalex.org/W1964965059","https://openalex.org/W1980388858","https://openalex.org/W1987822864","https://openalex.org/W2005987604","https://openalex.org/W2020873588","https://openalex.org/W2027950713","https://openalex.org/W2049932494","https://openalex.org/W2052469854","https://openalex.org/W2052673084","https://openalex.org/W2054174194","https://openalex.org/W2059721080","https://openalex.org/W2065054336","https://openalex.org/W2072419054","https://openalex.org/W2134065619","https://openalex.org/W2143005794","https://openalex.org/W2151715640","https://openalex.org/W2318231933","https://openalex.org/W2478289388","https://openalex.org/W4210592456"],"related_works":["https://openalex.org/W1964965059","https://openalex.org/W2318231933","https://openalex.org/W2151715640","https://openalex.org/W2020873588","https://openalex.org/W1980388858","https://openalex.org/W2122092051","https://openalex.org/W2071085691","https://openalex.org/W206245487","https://openalex.org/W2040632702","https://openalex.org/W2057797149","https://openalex.org/W2096675625","https://openalex.org/W1574043876","https://openalex.org/W2007148812","https://openalex.org/W2028775699","https://openalex.org/W1952341438","https://openalex.org/W589878631","https://openalex.org/W3209947603","https://openalex.org/W2314715369","https://openalex.org/W2020099046","https://openalex.org/W1963677918"],"abstract_inverted_index":{"\u00a71.":[0],"Introduction":[1],".":[2,76,110],"It":[3],"is":[4,79,97,146,157,188,194,197,201,203,209,215,219,221,227,236],"a":[5,100,204,222,232],"well-known":[6],"phenomenon":[7,63],"in":[8,13,65,69,108],"set":[9,94,101],"theory":[10,135],"that":[11],"problems":[12,29],"infinite":[14],"combinatorics":[15],"involving":[16],"singular":[17],"cardinals":[18],"and":[19,51,73,181],"their":[20],"successors":[21],"tend":[22],"to":[23],"be":[24],"harder":[25],"than":[26],"the":[27,35,40,43,46,52,103,119,141,171,210,228],"parallel":[28],"for":[30,61,231],"regular":[31],"cardinals.":[32],"Examples":[33,184],"include":[34,179,185],"behaviour":[36],"of":[37,42,48,54,83,95,102,121,140,150,175],"cardinal":[38,125,152],"exponentiation,":[39],"extent":[41,47],"tree":[44],"property,":[45],"stationary":[49],"reflection,":[50],"existence":[53],"non-free":[55],"almost-free":[56],"abelian":[57],"groups.":[58],"The":[59],"explanation":[60],"this":[62],"lies":[64],"inner":[66,81,133,148,161],"model":[67,82,134,149,162,230],"theory,":[68],"particular":[70],"core":[71,212,229],"models":[72],"covering":[74,128],"lemmas":[75],"If":[77],"W":[78,87,109,112,117],"an":[80,158],"V":[84,90,105,115,123,168],"then":[85,155],"1.":[86,186],"strongly":[88],"covers":[89,114,167],"if":[91,116],"every":[92,122],"uncountable":[93],"ordinals":[96],"covered":[98],"by":[99],"same":[104],"-cardinality":[106],"lying":[107],"2.":[111,199],"weakly":[113],"computes":[118],"successor":[120],"-singular":[124],"correctly.":[126],"Strong":[127],"implies":[129],"weak":[130],"covering.":[131],"In":[132],"there":[136,145,156],"are":[137],"many":[138],"theorems":[139],"general":[142],"form":[143],"\u201cif":[144],"no":[147],"large":[151],"hypothesis":[153],"X":[154,187,200,218],"L":[159,172],"-like":[160,173],"K":[163,176,192,207,225],"x":[164,177,193,208,226],"which":[165],"Y":[166,196,214,235],"\u201d.":[169],"Here":[170],"properties":[174],"always":[178],"GCH":[180],"Global":[182],"Square.":[183],"\u201c0":[189],"#":[190],"exists\u201d,":[191],"L,":[195],"\u201cstrongly\u201d.":[198,216],"\u201cthere":[202,220],"measurable":[205],"cardinal\u201d,":[206,224],"Dodd-Jensen":[211],"model,":[213],"3.":[217],"Woodin":[223,233],"cardinal,":[234],"\u201cweakly\u201d.":[237]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}