{"id":"https://openalex.org/W2085054174","doi":"https://doi.org/10.1305/ndjfl/1172787543","title":"Complexity Ranks of Countable Models","display_name":"Complexity Ranks of Countable Models","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2085054174","doi":"https://doi.org/10.1305/ndjfl/1172787543","mag":"2085054174"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1172787543","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1172787543","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal 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":null,"display_name":"Su Gao","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]},{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Su Gao","raw_affiliation_strings":["Department of Mathematics University of North Texas PO Box 311430 Denton TX 76203","University of Notre Dame"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of North Texas PO Box 311430 Denton TX 76203","institution_ids":["https://openalex.org/I123534392"]},{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I107639228","https://openalex.org/I123534392"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.15446044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"48","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9968000054359436,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.9450876712799072},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.926375150680542},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7783881425857544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6974622011184692},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4608258008956909},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4113992750644684},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.38277459144592285}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.9450876712799072},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.926375150680542},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7783881425857544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6974622011184692},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4608258008956909},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4113992750644684},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.38277459144592285}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1305/ndjfl/1172787543","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1172787543","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.630.3972","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.630.3972","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.unt.edu/~sgao/pub/paper25.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1172787543","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1172787543","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":[{"display_name":"Reduced inequalities","score":0.5600000023841858,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W40029885","https://openalex.org/W42390634","https://openalex.org/W965226192","https://openalex.org/W1483128311","https://openalex.org/W1565029977","https://openalex.org/W1565979850","https://openalex.org/W1602868010","https://openalex.org/W2019185145","https://openalex.org/W2119981307","https://openalex.org/W2163355682","https://openalex.org/W2575297946","https://openalex.org/W4293117209"],"related_works":["https://openalex.org/W3172619790","https://openalex.org/W2035456572","https://openalex.org/W2085054174","https://openalex.org/W2059675826","https://openalex.org/W3213392216","https://openalex.org/W3030465535","https://openalex.org/W2928935854","https://openalex.org/W2095282951","https://openalex.org/W4288376543","https://openalex.org/W2122650439"],"abstract_inverted_index":{"We":[0],"define":[1],"some":[2,13],"variations":[3],"of":[4,27,36],"the":[5,16,24,33,37],"Scott":[6],"rank":[7,26,35],"for":[8],"countable":[9],"models":[10],"and":[11],"obtain":[12],"inequalities":[14],"involving":[15],"ranks.":[17],"For":[18],"mono-unary":[19],"algebras":[20],"we":[21],"prove":[22],"that":[23],"game":[25,34],"any":[28],"subtree":[29],"does":[30],"not":[31],"exceed":[32],"whole":[38],"model.":[39],"However,":[40],"similar":[41],"questions":[42],"about":[43],"linear":[44],"orders":[45],"remain":[46],"unresolved.":[47]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
