{"id":"https://openalex.org/W1989095041","doi":"https://doi.org/10.2307/2273292","title":"<i>R</i>-maximal Boolean algebras","display_name":"<i>R</i>-maximal Boolean algebras","publication_year":1979,"publication_date":"1979-12-01","ids":{"openalex":"https://openalex.org/W1989095041","doi":"https://doi.org/10.2307/2273292","mag":"1989095041"},"language":"en","primary_location":{"id":"doi:10.2307/2273292","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273292","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/A5113511227","display_name":"Jeffrey B. Remmel","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. B. Remmel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5113511227"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6226,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61264911,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"44","issue":"4","first_page":"533","last_page":"548"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9979000091552734,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9979000091552734,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9921000003814697,"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/T11567","display_name":"semigroups and automata theory","score":0.9919000267982483,"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/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.9689141511917114},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.8260014057159424},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.6531258225440979},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6430302858352661},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5659707188606262},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.527877688407898},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.5228132009506226},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.4856947362422943},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4642741084098816},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.4332762360572815},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.4320200979709625},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.22315844893455505},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.21165427565574646},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.20838889479637146},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19151970744132996},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16886445879936218}],"concepts":[{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.9689141511917114},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.8260014057159424},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.6531258225440979},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6430302858352661},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5659707188606262},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.527877688407898},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.5228132009506226},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.4856947362422943},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4642741084098816},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.4332762360572815},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.4320200979709625},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.22315844893455505},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.21165427565574646},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.20838889479637146},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19151970744132996},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16886445879936218},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2273292","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273292","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/14","display_name":"Life below water"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1816556148","https://openalex.org/W1975466840","https://openalex.org/W2097898753","https://openalex.org/W2530006810","https://openalex.org/W2554842236","https://openalex.org/W2905135108"],"related_works":["https://openalex.org/W2037833610","https://openalex.org/W2135152748","https://openalex.org/W2069987267","https://openalex.org/W1973052363","https://openalex.org/W1972481159","https://openalex.org/W1980641386","https://openalex.org/W2112189052","https://openalex.org/W4249600134","https://openalex.org/W2757989085","https://openalex.org/W2000047385"],"abstract_inverted_index":{"Metakides":[0,25,74],"and":[1,26,50,53,75,80,88,92,106,136,140,146,156,160,186,246],"Nerode":[2,27],"in":[3,28,68],"[2]":[4],"suggested":[5],"the":[6,12,31,55,62,93,132,158,177,242],"study":[7],"of":[8,14,18,33,34,39,57,61,95,99,122,126,134,162,169,188,204,225,230,235,244],"what":[9],"they":[10],"termed":[11],"lattice":[13,32,56,94,240],"recursively":[15,20,41,58,96,102,114,206,221,232],"enumerable":[16,36,59,97,207,222,233],"substructures":[17],"a":[19,40,100,123,150,167,220,239],"presented":[21,42,103,115],"model.":[22],"For":[23],"example,":[24],"[3]":[29],"introduced":[30],"recusively":[35],"subspaces,":[37],",":[38,119,120,128,135,170,189,236,237],"vector":[43],"space":[44],"V":[45],"\u221e":[46],".":[47,163,182],"The":[48,228],"similarities":[49,87],"differences":[51,89],"between":[52,90],"\u2130,":[54],"subsets":[60],"natural":[63],"numbers":[64],"N":[65,127],"as":[66],"defined":[67],"[9],":[69],"have":[70],"been":[71],"studied":[72,85],"by":[73,180],"Nerode,":[76],"Kalantari,":[77],"Remmel,":[78],"Retzlaff,":[79],"Shore.":[81],"In":[82],"[6],":[83],"we":[84,171,190],"some":[86],"\u2130":[91],"sub-algebras":[98,184],"weakly":[101,113],"Boolean":[104,116,151],"algebra":[105,117],"this":[107],"paper":[108],"continues":[109],"that":[110],"study.":[111],"A":[112,201],"(W.R.P.B.A.)":[118],"consists":[121],"recursive":[124,145],"subset":[125,168,224],"\u2223":[129,213,214,226],"\u2223,":[130],"called":[131],"field":[133],"operations":[137,243],"(meet),":[138],"(join),":[139],"(complement)":[141],"which":[142,148],"are":[143],"partial":[144],"under":[147,241],"becomes":[149],"algebra.":[152],"We":[153],"shall":[154],"write":[155],"for":[157],"zero":[159],"unit":[161],"If":[164],"S":[165,174,181],"is":[166,205,219],"let":[172,191],"(":[173,196],")*":[175],"denote":[176,195],"subalgebra":[178,202],"generated":[179],"Given":[183],"B":[185,192,197,203,217],"C":[187,194,199],"+":[193],"\u22c3":[198],")*.":[200],"(recursive)":[208,223],"if":[209],"{":[210],"x":[211,215],"\u2208":[212,216],"}":[218],"\u2223.":[227],"set":[229],"all":[231],"subalgebras":[234],"forms":[238],"intersection":[245],"sum":[247],"(+).":[248]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
