{"id":"https://openalex.org/W2039872825","doi":"https://doi.org/10.2307/2273976","title":"On the number of generators of cylindric algebras","display_name":"On the number of generators of cylindric algebras","publication_year":1985,"publication_date":"1985-12-01","ids":{"openalex":"https://openalex.org/W2039872825","doi":"https://doi.org/10.2307/2273976","mag":"2039872825"},"language":"en","primary_location":{"id":"doi:10.2307/2273976","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273976","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/A5080876991","display_name":"Hajnal Andr\u00e9ka","orcid":"https://orcid.org/0000-0002-7327-4702"},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"H. Andr\u00e9ka","raw_affiliation_strings":["Mathematical Institute, Hungarian Academy of Sciences, Budapest, Hungary","Hungarian Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Hungarian Academy of Sciences, Budapest, Hungary","institution_ids":["https://openalex.org/I7597260"]},{"raw_affiliation_string":"Hungarian Academy of Sciences","institution_ids":["https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071216223","display_name":"I. N\u00e9meti","orcid":null},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"I. N\u00e9meti","raw_affiliation_strings":["Mathematical Institute, Hungarian Academy of Sciences, Budapest, Hungary","Hungarian Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Hungarian Academy of Sciences, Budapest, Hungary","institution_ids":["https://openalex.org/I7597260"]},{"raw_affiliation_string":"Hungarian Academy of Sciences","institution_ids":["https://openalex.org/I7597260"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7413,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79585461,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"50","issue":"4","first_page":"865","last_page":"873"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10215","display_name":"Semantic Web and Ontologies","score":0.9480999708175659,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9480999708175659,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9390000104904175,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9229000210762024,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.6849313974380493},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.64994215965271},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5176889896392822},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4504542946815491},{"id":"https://openalex.org/keywords/algebraic-logic","display_name":"Algebraic logic","score":0.45044341683387756},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4458949565887451},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.438802570104599},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.4224364757537842},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.41868066787719727},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.41452687978744507},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40910714864730835},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.379011332988739},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3677560091018677},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3235284984111786},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13735955953598022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6849313974380493},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.64994215965271},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5176889896392822},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4504542946815491},{"id":"https://openalex.org/C86523455","wikidata":"https://www.wikidata.org/wiki/Q1005222","display_name":"Algebraic logic","level":3,"score":0.45044341683387756},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4458949565887451},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.438802570104599},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.4224364757537842},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41868066787719727},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41452687978744507},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40910714864730835},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.379011332988739},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3677560091018677},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3235284984111786},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13735955953598022},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273976","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273976","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/1183741963","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183741963","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W16761111","https://openalex.org/W1528931898","https://openalex.org/W1756661417","https://openalex.org/W2087488578","https://openalex.org/W4248503953"],"related_works":["https://openalex.org/W178365807","https://openalex.org/W3035881305","https://openalex.org/W155209255","https://openalex.org/W2750830833","https://openalex.org/W2189295089","https://openalex.org/W4287634368","https://openalex.org/W3103359050","https://openalex.org/W2282765366","https://openalex.org/W4248181727","https://openalex.org/W4388404668"],"abstract_inverted_index":{"The":[0,161,183,280,353],"theory":[1,9,35,311,339],"of":[2,10,25,32,50,118,129,137,141,155,195,204,240,249,269,272,278,308,327,343,349,367,372],"cylindric":[3,139,207,211,215],"algebras":[4,65,140,213,217],"(CA's)":[5],"is":[6,220,258,265,332,345,357],"the":[7,23,61,114,119,127,135,156,202,266,316,322,334,370,373],"algebraic":[8,267],"first":[11,76,95,273],"order":[12,77,96,274],"logics.":[13],"Several":[14],"ideas":[15,43],"about":[16,44,100],"logic":[17,78],"are":[18,28,200,233,369],"easier":[19],"to":[20,74,81,314,362,379],"formulate":[21],"in":[22,94,170,193,222,245,304,325,347],"frame":[24],"CA-theory.":[26],"Such":[27],"e.g.":[29],"some":[30],"concepts":[31,117,344,371],"abstract":[33,309],"model":[34,310],"(cf.":[36,54,276],"[1]":[37],"and":[38,56,66,108,116,123,188,214,238,247,301,376],"[10]\u2013[12])":[39],"as":[40,42],"well":[41],"relationships":[45],"between":[46,63],"several":[47,82],"axiomatic":[48],"theories":[49,360],"different":[51],"similarity":[52],"types":[53],"[4]":[55],"[10]).":[57],"In":[58,306,336],"contrast":[59],"with":[60,355],"relationship":[62],"Boolean":[64],"classical":[67,75],"propositional":[68],"logic,":[69],"CA's":[70,364],"correspond":[71,361],"not":[72],"only":[73],"but":[79],"also":[80],"other":[83],"ones.":[84],"Hence":[85],"CA-theoretic":[86],"results":[87],"contain":[88],"more":[89,99],"information":[90],"than":[91],"their":[92],"counterparts":[93],"logic.":[97],"For":[98,318],"this":[101,312],"see":[102],"[1],":[103],"[3],":[104],"[5],":[105],"[9],":[106],"[10]":[107],"[12].":[109],"Here":[110],"we":[111,150],"shall":[112,151],"use":[113],"notation":[115],"monographs":[120],"Henkin-Monk-Tarski":[121],"[7]":[122,250,328],"[8].":[124],"\u03c9":[125,181],"denotes":[126,134],"set":[128,208,212,216,342],"natural":[130],"numbers.":[131],"CA":[132,147,158,166,228,286],"\u03b1":[133,143,148,159,164,167,175,179,186,190,229,257,287],"class":[136,157,162],"all":[138,205],"dimension":[142],";":[144],"by":[145,235,260,294],"\u201ca":[146],"\u201d":[149],"understand":[152],"an":[153],"element":[154],".":[160,182,230],"Dc":[163,174,256],"\u2286":[165,227],"was":[168,243],"defined":[169,192],"[7].":[171],"Note":[172],"that":[173,226,251,358],"=":[176],"0":[177],"for":[178,283],"\u2208":[180],"classes":[184,203],"Ws":[185],",":[187],"Cs":[189],"were":[191],"1.1.1":[194],"[8],":[196],"p.":[197,299],"4.":[198],"They":[199],"called":[201],"weak":[206],"algebras,":[209],"regular":[210],"respectively.":[218],"It":[219,242],"proved":[221,244],"[8]":[223],"(I.7.13,":[224],"I.1.9)":[225],"(These":[231],"inclusions":[232],"proper":[234],"7.3.7,":[236],"1.4.3":[237],"1.5.3":[239],"[8].)":[241],"2.3.22":[246],"2.3.23":[248,277,326],"every":[252],"simple,":[253],"finitely":[254],"generated":[255,259],"a":[261,270,295,350],"single":[262,296,351],"element.":[263],"This":[264,330],"counterpart":[268],"property":[271,323,331],"logics":[275,320],"[7]).":[279,305],"question":[281],"arose:":[282],"which":[284,319,368],"simple":[285,363],"'s":[288],"does":[289,321],"\u201cfinitely":[290],"generated\u201d":[291],"imply":[292],"\u201cgenerated":[293],"element\u201d":[297],"(see":[298],"291":[300],"Problem":[302],"2.3":[303],"terms":[307,348],"amounts":[313],"asking":[315],"question:":[317],"described":[324],"hold?":[329],"roughly":[333],"following.":[335],"any":[337,340],"maximal":[338,359],"finite":[341],"definable":[346],"concept.":[352],"connection":[354],"CA-theory":[356],"(the":[365],"elements":[366],"original":[374],"logic)":[375],"definability":[377],"corresponds":[378],"generation.":[380]},"counts_by_year":[{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}