{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:02:09Z","timestamp":1649030529005},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3206,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2005,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Non-perfect separably closed fields are stable, and not superstable. As a result, not all types can be ranked. We develop here a new tool, a \u201csemi-rank\u201d, which takes values in the non-negative reals, and gives a sufficient condition for forking of types. This semi-rank is built up from a transcendence function, analogous to the one considered by Kolehin in the context of differentially closed fields. It yields some orthogonality and stratification results.<\/jats:p>","DOI":"10.2178\/jsl\/1120224735","type":"journal-article","created":{"date-parts":[[2005,7,1]],"date-time":"2005-07-01T15:07:20Z","timestamp":1120230440000},"page":"664-680","source":"Crossref","is-referenced-by-count":0,"title":["Une fonction de Kolchin pour les corps imparfaits de degr\u00e9 d'imperfection fini"],"prefix":"10.1017","volume":"70","author":[{"given":"Fran\u00e7oise","family":"Delon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200007143_ref007","first-page":"1443","volume":"65","author":"Chatzidakis","year":"2000","journal-title":"Minimal types in separably closed fields"},{"key":"S0022481200007143_ref011","volume-title":"Algebra","author":"Lang","year":"1978"},{"key":"S0022481200007143_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-01-02886-0"},{"key":"S0022481200007143_ref015","volume-title":"Classification Theory","author":"Shelah","year":"1990"},{"key":"S0022481200007143_ref014","first-page":"347","volume":"65","author":"Pong","year":"2000","journal-title":"Some applications of ordinal dimensions to the theory of differential closed fields"},{"key":"S0022481200007143_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07330-8"},{"key":"S0022481200007143_ref008","article-title":"Id\u00e9aux et types sur les corps s\u00e9parablement clos","volume":"116","author":"Delon","year":"1988","journal-title":"Suppl\u00e9ment au Bulletin de la Soci\u00e9t\u00e9 Math\u00e9matique de France, M\u00e9moire 33"},{"key":"S0022481200007143_ref002","first-page":"1178","volume":"67","author":"Benoist","year":"2002","journal-title":"Rungs et types g\u00e9n\u00e9riques dans les corps diff\u00e9rentiellement clos"},{"key":"S0022481200007143_ref003","unstructured":"Blossier Thomas , Ensembles minimaux localement modulaires, Ph.D. thesis, Universit\u00e9 Paris 7-Denis Diderot, 2001."},{"key":"S0022481200007143_ref010","volume-title":"Differential Algebra and Algebraic Groups","author":"Kolchin","year":"1973"},{"key":"S0022481200007143_ref004","volume-title":"Annals of Pure and Applied Logic","author":"Blossier"},{"key":"S0022481200007143_ref009","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-68521-0_9","volume-title":"Model Theory and Algebraic Geometry","volume":"1696","author":"Delon","year":"1998"},{"key":"S0022481200007143_ref012","volume-title":"Stability in model theory","author":"Lascar","year":"1987"},{"key":"S0022481200007143_ref013","unstructured":"Pong Wai Yan , Ordinal dimensions and differential completeness, Ph.D. thesis, University of Illinois, Chicago, 2000."},{"key":"S0022481200007143_ref006","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0082232","volume-title":"Classification Theory","volume":"1292","author":"Chatzidakis","year":"1987"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200007143","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T20:50:05Z","timestamp":1556916605000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200007143\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2005,6]]}},"alternative-id":["S0022481200007143"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1120224735","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6]]}}}