{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T06:20:31Z","timestamp":1772518831109,"version":"3.50.1"},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5124,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2000,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Using the Lascar inequalities, we show that any finite rank \u03b4-closed subset of a quasiprojective variety is definably isomorphic to an affine \u03b4-closed set. Moreover, we show that if <jats:italic>X<\/jats:italic> is a finite rank subset of the projective space \u2119<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> and a is <jats:bold>a<\/jats:bold> generic point of \u2119<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>, then the projection from a is injective on <jats:italic>X<\/jats:italic>. Finally we prove that if RM = RC in DCF<jats:sub>0<\/jats:sub>, then RM = RU.<\/jats:p>","DOI":"10.2307\/2586542","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T14:01:31Z","timestamp":1146924091000},"page":"347-356","source":"Crossref","is-referenced-by-count":6,"title":["Some applications of ordinal dimensions to the theory of differentially closed fields"],"prefix":"10.1017","volume":"65","author":[{"given":"Wai Yan","family":"Pong","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200012524_ref008","volume-title":"Stability in model theory","volume":"36","author":"Lascar","year":"1987"},{"key":"S0022481200012524_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757234"},{"key":"S0022481200012524_ref011","first-page":"114","volume-title":"Differential Algebraic Groups and the Number of Countable Differentially Closed Fields","author":"Pillay","year":"1996"},{"key":"S0022481200012524_ref003","volume-title":"Minimal subsets of differentially closed fields","author":"Hrushovski"},{"key":"S0022481200012524_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22174-7_2"},{"key":"S0022481200012524_ref013","first-page":"1379","volume":"49","author":"Saffe","year":"1984","journal-title":"Categoricity and ranks"},{"key":"S0022481200012524_ref006","volume-title":"Differential algebra and algebraic groups","volume":"54","author":"Kolchin","year":"1973"},{"key":"S0022481200012524_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574"},{"key":"S0022481200012524_ref002","author":"Hrushovski","journal-title":"Lascar rank Morley rank differ in differentially closed fields"},{"key":"S0022481200012524_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/2373279"},{"key":"S0022481200012524_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02564523"},{"key":"S0022481200012524_ref010","unstructured":"McGrail T. , Model-theoretic results on ordinary and partial differential fields, Ph.D. thesis , Wesleyan University, 1997."},{"key":"S0022481200012524_ref012","unstructured":"Pong W.Y. , Ordinal dimensions and differential completeness, Ph.D. thesis , University of Illinois at Chicago, 1999."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200012524","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T15:08:35Z","timestamp":1557414515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200012524\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,3]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2000,3]]}},"alternative-id":["S0022481200012524"],"URL":"https:\/\/doi.org\/10.2307\/2586542","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,3]]}}}