{"id":"https://openalex.org/W2140488850","doi":"https://doi.org/10.1142/s0219061302000084","title":"KNIGHT'S MODEL, ITS AUTOMORPHISM GROUP, AND CHARACTERIZING THE UNCOUNTABLE CARDINALS","display_name":"KNIGHT'S MODEL, ITS AUTOMORPHISM GROUP, AND CHARACTERIZING THE UNCOUNTABLE CARDINALS","publication_year":2002,"publication_date":"2002-05-01","ids":{"openalex":"https://openalex.org/W2140488850","doi":"https://doi.org/10.1142/s0219061302000084","mag":"2140488850"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061302000084","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061302000084","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical 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/A5044036779","display_name":"Greg Hjorth","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"GREG HJORTH","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044036779"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.2203498,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"02","issue":"01","first_page":"113","last_page":"144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"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":0.9997000098228455,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9937999844551086,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9934999942779541,"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/uncountable-set","display_name":"Uncountable set","score":0.8281981945037842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.81524658203125},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.8128658533096313},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.6899200677871704},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6192135810852051},{"id":"https://openalex.org/keywords/knight","display_name":"Knight","score":0.6076667904853821},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.5334316492080688},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5181290507316589},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5154698491096497},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4445478320121765},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41492849588394165},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09992092847824097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06619042158126831}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.8281981945037842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.81524658203125},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8128658533096313},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.6899200677871704},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6192135810852051},{"id":"https://openalex.org/C71140485","wikidata":"https://www.wikidata.org/wiki/Q2943226","display_name":"Knight","level":2,"score":0.6076667904853821},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.5334316492080688},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5181290507316589},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5154698491096497},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4445478320121765},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41492849588394165},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09992092847824097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06619042158126831},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219061302000084","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061302000084","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical 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":9,"referenced_works":["https://openalex.org/W1542554317","https://openalex.org/W1658875765","https://openalex.org/W1978325228","https://openalex.org/W2019185145","https://openalex.org/W2087182292","https://openalex.org/W2090247723","https://openalex.org/W2163355682","https://openalex.org/W2575297946","https://openalex.org/W2963018530"],"related_works":["https://openalex.org/W2081974092","https://openalex.org/W4298487995","https://openalex.org/W1543499813","https://openalex.org/W2492302213","https://openalex.org/W1987207290","https://openalex.org/W2093379471","https://openalex.org/W2061834030","https://openalex.org/W4245799073","https://openalex.org/W2140488850","https://openalex.org/W1996617996"],"abstract_inverted_index":{"We":[0,44],"show":[1],"that":[2],"every":[3],"\u2135":[4,30],"\u03b1":[5],"(\u03b1&lt;\u03c9":[6],"1":[7,31],")":[8],"can":[9],"be":[10],"characterized":[11],"by":[12],"the":[13,37,55],"Scott":[14,27],"sentence":[15,28],"of":[16,58],"some":[17,46],"countable":[18,24],"model;":[19],"moreover":[20],"there":[21],"is":[22],"a":[23],"structure":[25],"whose":[26,33],"characterizes":[29],"but":[32],"automorphism":[34,56],"group":[35,57],"fails":[36],"topological":[38],"Vaught":[39],"conjecture":[40],"on":[41,49],"analytic":[42],"sets.":[43],"obtain":[45],"partial":[47],"information":[48],"Ulm":[50],"type":[51],"dichotomy":[52],"theorems":[53],"for":[54],"Knight's":[59],"model.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
