{"id":"https://openalex.org/W2106044804","doi":"https://doi.org/10.2178/jsl/1190150160","title":"Sequences of <i>n</i>-diagrams","display_name":"Sequences of <i>n</i>-diagrams","publication_year":2002,"publication_date":"2002-09-01","ids":{"openalex":"https://openalex.org/W2106044804","doi":"https://doi.org/10.2178/jsl/1190150160","mag":"2106044804"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150160","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150160","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/A5071875842","display_name":"Valentina Harizanov","orcid":"https://orcid.org/0000-0002-6626-5074"},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Valentina S. Harizanov","raw_affiliation_strings":["Department of Mathematics, The George Washington University, Washington, D.C. 20052, USA, E-mail:","the George Washington University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The George Washington University, Washington, D.C. 20052, USA, E-mail:","institution_ids":["https://openalex.org/I193531525"]},{"raw_affiliation_string":"the George Washington University","institution_ids":["https://openalex.org/I193531525"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112811349","display_name":"Julia F. Knight","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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Julia F. Knight","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA, E-mail:","University of Notre Dame"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA, E-mail:","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080060901","display_name":"Andrey Morozov","orcid":"https://orcid.org/0000-0001-8647-5629"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Andrei S. Morozov","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia, E-mail:","Sobolev Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia, E-mail:","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics","institution_ids":["https://openalex.org/I4210096862"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6921,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.69390186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"67","issue":"3","first_page":"1227","last_page":"1247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"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":0.9980000257492065,"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/countable-set","display_name":"Countable set","score":0.8597220182418823},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.7165685296058655},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6355098485946655},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5777875781059265},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5682527422904968},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5309944152832031},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4155803620815277},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22741875052452087},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.0535891056060791}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8597220182418823},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.7165685296058655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6355098485946655},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5777875781059265},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5682527422904968},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5309944152832031},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4155803620815277},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22741875052452087},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0535891056060791},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1190150160","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150160","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/1190150160","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150160","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":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W93165072","https://openalex.org/W1974760368","https://openalex.org/W1976089169","https://openalex.org/W1982821787","https://openalex.org/W2015393409","https://openalex.org/W2039687554","https://openalex.org/W2146750910","https://openalex.org/W2159037930","https://openalex.org/W2333530874","https://openalex.org/W6702750620"],"related_works":["https://openalex.org/W1631776469","https://openalex.org/W2950866767","https://openalex.org/W4299610791","https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W3106300234","https://openalex.org/W2473730886","https://openalex.org/W2541640833","https://openalex.org/W4206367340","https://openalex.org/W1606946808"],"abstract_inverted_index":{"We":[0,24,56],"consider":[1],"only":[2],"computable":[3],"languages,":[4],"and":[5,44,67,138],"countable":[6],"structures,":[7],"with":[8,27,101],"universe":[9],"a":[10,20,33,78,106],"subset":[11],"of":[12,18,22,53,97],"\u03c9":[13,54],",":[14,35,87,91,130,137],"which":[15],"we":[16,113],"think":[17],"as":[19,59],"set":[21],"constants.":[23],"identify":[25],"sentences":[26],"their":[28],"G\u00f6del":[29],"numbers.":[30],"Thus,":[31],"for":[32],"structure":[34],"the":[36,45,117],"complete":[37],"(elementary)":[38],"diagram,":[39,47],"D":[40,48],"c":[41],"(":[42,49],"),":[43,50],"atomic":[46],"are":[51],"subsets":[52],".":[55],"classify":[57],"formulas":[58],"usual.":[60],"A":[61],"formula":[62,107,119],"is":[63,72,84,121,127,134],"both":[64],"\u03a3":[65,85,128],"0":[66,69],"\u03a0":[68,89,135],"if":[70,92],"it":[71,93],"open.":[73],"For":[74,105],"n":[75,86,90,95,129,136],"&gt;":[76],"0,":[77],"formula,":[79],"in":[80,109],"prenex":[81,110],"normal":[82,111],"form,":[83,112],"or":[88,103],"has":[94],"blocks":[96],"like":[98],"quantifiers,":[99],"beginning":[100],"\u2203,":[102],"\u2200.":[104],"\u03b8,":[108],"let":[114],"neg(\u03b8)":[115],"denote":[116],"dual":[118],"that":[120],"logically":[122],"equivalent":[123],"to":[124],"\u00ac\u03b8\u2014if":[125],"\u03b8":[126],"then":[131],"neg":[132],"(\u03b8)":[133],"vice":[139],"versa.":[140]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
