{"id":"https://openalex.org/W2146314802","doi":"https://doi.org/10.1145/2733376","title":"On the Variable Hierarchy of First-Order Spectra","display_name":"On the Variable Hierarchy of First-Order Spectra","publication_year":2015,"publication_date":"2015-03-21","ids":{"openalex":"https://openalex.org/W2146314802","doi":"https://doi.org/10.1145/2733376","mag":"2146314802"},"language":"en","primary_location":{"id":"doi:10.1145/2733376","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2733376","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational 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/A5107269947","display_name":"Eryk Kopczy\u0144ski","orcid":"https://orcid.org/0000-0001-5588-1181"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Eryk Kopczy\u0144ski","raw_affiliation_strings":["University of Warsaw"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warsaw","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060686021","display_name":"Tony Tan","orcid":"https://orcid.org/0009-0005-8341-2004"},"institutions":[{"id":"https://openalex.org/I878454856","display_name":"Hasselt University","ror":"https://ror.org/04nbhqj75","country_code":"BE","type":"education","lineage":["https://openalex.org/I878454856"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Tony Tan","raw_affiliation_strings":["Hasselt University and Transnational University of Limburg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hasselt University and Transnational University of Limburg","institution_ids":["https://openalex.org/I878454856"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5107269947"],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":null,"apc_paid":null,"fwci":0.3634,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66383994,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":"2","first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9901999831199646,"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/T11567","display_name":"semigroups and automata theory","score":0.9901999831199646,"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/T12029","display_name":"DNA and Biological Computing","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9797000288963318,"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/hierarchy","display_name":"Hierarchy","score":0.8334164023399353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7388893365859985},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.7374163866043091},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.6080648303031921},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5397106409072876},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5089001655578613},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.4956856966018677},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48868635296821594},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4804939031600952},{"id":"https://openalex.org/keywords/spectral-line","display_name":"Spectral line","score":0.46074333786964417},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.44457748532295227},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4278859794139862},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3932730555534363},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3471032381057739},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13561517000198364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10723811388015747},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07657331228256226},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07286825776100159},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06409743428230286}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.8334164023399353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7388893365859985},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.7374163866043091},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.6080648303031921},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5397106409072876},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5089001655578613},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4956856966018677},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48868635296821594},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4804939031600952},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.46074333786964417},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.44457748532295227},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4278859794139862},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3932730555534363},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3471032381057739},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13561517000198364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10723811388015747},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07657331228256226},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07286825776100159},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06409743428230286},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2733376","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2733376","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"},{"id":"pmh:oai:documentserver.uhasselt.be:1942/18319","is_oa":false,"landing_page_url":"http://hdl.handle.net/1942/18319","pdf_url":null,"source":{"id":"https://openalex.org/S4306401926","display_name":"Document Server@UHasselt (UHasselt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I878454856","host_organization_name":"Hasselt University","host_organization_lineage":["https://openalex.org/I878454856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G4392507518","display_name":null,"funder_award_id":"DEC 2012/07/D/ST6/02435","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1507717186","https://openalex.org/W1527197079","https://openalex.org/W1980879781","https://openalex.org/W1987681136","https://openalex.org/W2004663163","https://openalex.org/W2006484856","https://openalex.org/W2007053458","https://openalex.org/W2031764672","https://openalex.org/W2033743662","https://openalex.org/W2043071947","https://openalex.org/W2044122859","https://openalex.org/W2065706312","https://openalex.org/W2082778556","https://openalex.org/W2130190334","https://openalex.org/W2142482847","https://openalex.org/W2319050586","https://openalex.org/W2964224456","https://openalex.org/W3127113455","https://openalex.org/W4230783973","https://openalex.org/W4236835455","https://openalex.org/W4298227433","https://openalex.org/W4301523176","https://openalex.org/W4391177866"],"related_works":["https://openalex.org/W2365264209","https://openalex.org/W2509431957","https://openalex.org/W2026999166","https://openalex.org/W2382566571","https://openalex.org/W1599954583","https://openalex.org/W1992685502","https://openalex.org/W4211007821","https://openalex.org/W2802395037","https://openalex.org/W4389565704","https://openalex.org/W2349321798"],"abstract_inverted_index":{"The":[0],"spectrum":[1],"of":[2,10,16,27,34,74],"a":[3],"first-order":[4,28,75],"logic":[5],"sentence":[6],"is":[7,77,82],"the":[8,25,32,48,57,72],"set":[9],"natural":[11],"numbers":[12],"that":[13,40,59,68],"are":[14],"cardinalities":[15],"its":[17],"finite":[18],"models.":[19],"In":[20],"this":[21],"article,":[22],"we":[23,66],"study":[24],"hierarchy":[26],"spectra":[29,76],"based":[30],"on":[31],"number":[33],"variables.":[35,45],"It":[36],"has":[37],"been":[38],"conjectured":[39],"it":[41,50,81],"collapses":[42],"to":[43,69,84],"three":[44,89],"We":[46],"show":[47,67],"opposite:":[49],"forms":[51],"an":[52],"infinite":[53],"hierarchy.":[54],"However,":[55],"despite":[56],"fact":[58],"more":[60,64],"variables":[61,90],"can":[62],"express":[63],"spectra,":[65],"establish":[70],"whether":[71],"class":[73],"closed":[78],"under":[79],"complement,":[80],"sufficient":[83],"consider":[85],"sentences":[86],"using":[87],"only":[88],"and":[91],"binary":[92],"relations.":[93]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
