{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T19:27:43Z","timestamp":1655148463212},"reference-count":10,"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":4210,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is known that in differentially closed fields of characteristic zero, the ranks of stability <jats:italic>RU, RM<\/jats:italic> and the topological rank <jats:italic>RH<\/jats:italic> need not to be equal. Pillay and Pong have just shown however that the ranks <jats:italic>RU<\/jats:italic> and <jats:italic>RM<\/jats:italic> coincide in a group definable in this theory. At the opposite, we will show in this paper that the ranks <jats:italic>RM<\/jats:italic> and <jats:italic>RH<\/jats:italic> of a definable group can also be different, and even lead to non-equivalent notions of generic type.<\/jats:p>","DOI":"10.2178\/jsl\/1190150157","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:14:26Z","timestamp":1197555266000},"page":"1178-1188","source":"Crossref","is-referenced-by-count":3,"title":["Rangs et types de rang maximum dans les corps diff\u00e9rentiellement clos"],"prefix":"10.1017","volume":"67","author":[{"given":"Franck","family":"Benoist","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009506_ref008","volume-title":"Groupes stables","author":"Poizat","year":"1987"},{"key":"S0022481200009506_ref007","volume-title":"Cours de th\u00e9orie des mod\u00e8les","author":"Poizat","year":"1987"},{"key":"S0022481200009506_ref005","doi-asserted-by":"crossref","unstructured":"Pillay Anand et Pong Wai Yan , On Lascar rank and Morley rank of definable groups in the theory of differentially closed fields, 2001, manuscrit.","DOI":"10.2178\/jsl\/1190150158"},{"key":"S0022481200009506_ref004","first-page":"1138","volume":"55","author":"Pillay","year":"1990","journal-title":"Differential algebraic group chunks"},{"key":"S0022481200009506_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22174-7_2"},{"key":"S0022481200009506_ref002","first-page":"1280","volume":"64","author":"Hrushovski","year":"1999","journal-title":"Lascar and Morley ranks differ in differentially closed fields"},{"key":"S0022481200009506_ref009","volume-title":"Ordinal dimensions and differential completeness","author":"Pong","year":"1999"},{"key":"S0022481200009506_ref006","volume-title":"Th\u00e9ories stables. I\u00e8re ann\u00e9e. 1977\/78","author":"Poizat","year":"1978"},{"key":"S0022481200009506_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/033"},{"key":"S0022481200009506_ref001","volume-title":"Transactions of the American Mathematical Society","author":"Bousearen"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T20:45:03Z","timestamp":1557175503000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009506\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,9]]}},"alternative-id":["S0022481200009506"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150157","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}