{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T00:31:28Z","timestamp":1773966688892,"version":"3.50.1"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":923,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2011,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is known that for all finite <jats:italic>n<\/jats:italic> \u2265 5, there are relation algebras with <jats:italic>n<\/jats:italic>-dimensional relational bases but no weak representations. We prove that conversely, there are finite weakly representable relation algebras with no <jats:italic>n<\/jats:italic>-dimensional relational bases. In symbols: neither of the classes RA<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> and wRRA contains the other.<\/jats:p>","DOI":"10.2178\/jsl\/1309952524","type":"journal-article","created":{"date-parts":[[2011,7,6]],"date-time":"2011-07-06T07:42:35Z","timestamp":1309938155000},"page":"870-882","source":"Crossref","is-referenced-by-count":1,"title":["Weak representations of relation algebras and relational bases"],"prefix":"10.1017","volume":"76","author":[{"given":"Robin","family":"Hirsch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ian","family":"Hodkinson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roger D.","family":"Maddux","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200001560_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/1993545"},{"key":"S0022481200001560_ref008","first-page":"245","volume-title":"Algebraic logic","volume":"54","author":"J\u00f3nsson","year":"1991"},{"key":"S0022481200001560_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90055-6"},{"key":"S0022481200001560_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190815"},{"key":"S0022481200001560_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-009-2103-7"},{"key":"S0022481200001560_ref013","volume-title":"Relation algebras","volume":"150","author":"Maddux","year":"2006"},{"key":"S0022481200001560_ref012","first-page":"1213","volume":"57","author":"Maddux","year":"1992","journal-title":"Relation algebras of every dimension"},{"key":"S0022481200001560_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190416"},{"key":"S0022481200001560_ref004","volume-title":"Relation algebras by games","volume":"147","author":"Hirsch","year":"2002"},{"key":"S0022481200001560_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050150"},{"key":"S0022481200001560_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-04-03743-2"},{"key":"S0022481200001560_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1982-0662049-7"},{"key":"S0022481200001560_ref014","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1307\/mmj\/1028999131","article-title":"On representable relation algebras","volume":"11","author":"Monk","year":"1964","journal-title":"Michigan Mathematics Journal"},{"key":"S0022481200001560_ref016","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/041"},{"key":"S0022481200001560_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1987-15483-8"},{"key":"S0022481200001560_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/1969375"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200001560","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T01:56:31Z","timestamp":1556330191000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200001560\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["S0022481200001560"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1309952524","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9]]}}}