{"id":"https://openalex.org/W2171795611","doi":"https://doi.org/10.2178/bsl/1182353852","title":"Groups and Algebras of Binary Relations","display_name":"Groups and Algebras of Binary Relations","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2171795611","doi":"https://doi.org/10.2178/bsl/1182353852","mag":"2171795611"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1182353852","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1182353852","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin 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/A5073363662","display_name":"Steven Givant","orcid":null},"institutions":[{"id":"https://openalex.org/I91481961","display_name":"Mills College","ror":"https://ror.org/01ynb8e46","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129","https://openalex.org/I91481961"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven Givant","raw_affiliation_strings":["Department of Mathematics and Computer Science, Mills College, 5000 Macarthur Boulevard, Oakland, CA 94613, USAE-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Mills College, 5000 Macarthur Boulevard, Oakland, CA 94613, USAE-mail:","institution_ids":["https://openalex.org/I91481961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080876991","display_name":"Hajnal Andr\u00e9ka","orcid":"https://orcid.org/0000-0002-7327-4702"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"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":"Hajnal Andr\u00e9ka","raw_affiliation_strings":["R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest P. O. Box 127, H-1364 Hungary, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest P. O. Box 127, H-1364 Hungary, E-mail:","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4265,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.73030166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"8","issue":"1","first_page":"38","last_page":"64"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9955000281333923,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9955000281333923,"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":0.9768999814987183,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9718000292778015,"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/binary-relation","display_name":"Binary relation","score":0.8505486249923706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.801783561706543},{"id":"https://openalex.org/keywords/relation-algebra","display_name":"Relation algebra","score":0.75084388256073},{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.7278298139572144},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.6474517583847046},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6286327242851257},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5945344567298889},{"id":"https://openalex.org/keywords/binary-operation","display_name":"Binary operation","score":0.5416361093521118},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4959340989589691},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4647008776664734},{"id":"https://openalex.org/keywords/interior-algebra","display_name":"Interior algebra","score":0.4438264071941376},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41201460361480713},{"id":"https://openalex.org/keywords/non-associative-algebra","display_name":"Non-associative algebra","score":0.3680265545845032},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3082793354988098},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.21144351363182068},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.16442641615867615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07378068566322327}],"concepts":[{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.8505486249923706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.801783561706543},{"id":"https://openalex.org/C10282146","wikidata":"https://www.wikidata.org/wiki/Q5965969","display_name":"Relation algebra","level":5,"score":0.75084388256073},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.7278298139572144},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.6474517583847046},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6286327242851257},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5945344567298889},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.5416361093521118},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4959340989589691},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4647008776664734},{"id":"https://openalex.org/C203254541","wikidata":"https://www.wikidata.org/wiki/Q10894825","display_name":"Interior algebra","level":5,"score":0.4438264071941376},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41201460361480713},{"id":"https://openalex.org/C518143113","wikidata":"https://www.wikidata.org/wiki/Q4391941","display_name":"Non-associative algebra","level":4,"score":0.3680265545845032},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3082793354988098},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.21144351363182068},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.16442641615867615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07378068566322327},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/bsl/1182353852","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1182353852","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1182353852","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1182353852","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":"publishedVersion","is_accepted":true,"is_published":true,"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":20,"referenced_works":["https://openalex.org/W190595227","https://openalex.org/W898052787","https://openalex.org/W1784765900","https://openalex.org/W1992205482","https://openalex.org/W2006006495","https://openalex.org/W2031325588","https://openalex.org/W2033274602","https://openalex.org/W2033831844","https://openalex.org/W2056017060","https://openalex.org/W2085054257","https://openalex.org/W2124361119","https://openalex.org/W2315064349","https://openalex.org/W3014083718","https://openalex.org/W3021659953","https://openalex.org/W3145287507","https://openalex.org/W4234122916","https://openalex.org/W4234491120","https://openalex.org/W6664526522","https://openalex.org/W6776836306","https://openalex.org/W6816464866"],"related_works":["https://openalex.org/W3006599641","https://openalex.org/W4237079078","https://openalex.org/W4244314978","https://openalex.org/W63408870","https://openalex.org/W591875192","https://openalex.org/W2742509483","https://openalex.org/W4230589130","https://openalex.org/W2171795611","https://openalex.org/W3037203475","https://openalex.org/W2566427880"],"abstract_inverted_index":{"Abstract":[0],"In":[1,91],"1941,":[2],"Tarski":[3],"published":[4],"an":[5],"abstract,":[6],"finitely":[7,84],"axiomatized":[8],"version":[9],"of":[10,13,19,28,39,53,99,103,110,115,121,124,138,146,151,153,162,205,219,223],"the":[11,17,65,76,100,186,203,220],"theory":[12,18,31],"binary":[14,40,139,163,224],"relations,":[15,140,164],"called":[16],"relation":[20,55,128,168,177,198,216],"algebras":[21,129,137,161,169,217,222],".":[22],"He":[23,42],"asked":[24],"whether":[25],"every":[26,175],"model":[27],"his":[29],"abstract":[30,54],"could":[32],"be":[33],"represented":[34],"as":[35,107,109,170],"a":[36,96,119,154,180,196,207],"concrete":[37,122],"algebra":[38,178],"relations.":[41,225],"and":[43,105,148,165,191],"J\u00f3nsson":[44,104,190],"obtained":[45],"some":[46,111],"initial,":[47],"positive":[48,101,208],"results":[49,102,114],"for":[50],"special":[51],"classes":[52],"algebras.":[56],"But":[57],"Lyndon":[58],"showed,":[59],"in":[60,63,134],"1950,":[61],"that":[62,75,174],"general":[64],"answer":[66,77],"to":[67,88,136,195,210],"Tarski's":[68,89,125,211],"question":[69],"is":[70],"negative.":[71],"Monk":[72],"proved":[73],"later":[74],"remains":[78],"negative":[79],"even":[80],"if":[81],"one":[82],"adjoins":[83],"many":[85,166],"new":[86],"axioms":[87],"system.":[90],"this":[92],"paper":[93],"we":[94],"describe":[95],"far-reaching":[97],"generalization":[98],"Tarski,":[106],"well":[108],"later,":[112],"related":[113],"Maddux.":[116],"We":[117,172],"construct":[118],"class":[120],"models":[123,158],"axioms\u2014called":[126],"coset":[127,197,215],"\u2014that":[130],"are":[131,142],"very":[132],"close":[133],"spirit":[135],"but":[141],"built":[143],"using":[144,214],"systems":[145],"groups":[147],"cosets":[149],"instead":[150,218],"elements":[152],"base":[155],"set.":[156],"The":[157,200],"include":[159],"all":[160],"non-representable":[167],"well.":[171],"prove":[173],"atomic":[176],"satisfying":[179],"certain":[181],"measurability":[182],"condition\u2014a":[183],"condition":[184],"generalizing":[185],"conditions":[187],"imposed":[188],"by":[189,213],"Tarski\u2014is":[192],"essentially":[193],"isomorphic":[194],"algebra.":[199],"theorem":[201],"raises":[202],"possibility":[204],"providing":[206],"solution":[209],"problem":[212],"standard":[221]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
