{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T10:22:25Z","timestamp":1706178145093},"reference-count":19,"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":2841,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2006,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006216_inline1\" \/>be the category of all reduced compact complex spaces, viewed as a multi-sorted first order structure, in the standard way. Let<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006216_inline2\" \/>be a sub-category of<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006216_inline1\" \/>. which is closed under the taking of products and analytic subsets, and whose morphisms include the projections. Under the assumption that Th(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006216_inline2\" \/>) is unidimensional. we show that Morley rank is equal to Noetherian dimension, in any elementary extension of<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006216_inline2\" \/>. As a result, we are able to show that Morley degree is definable in Th(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006216_inline2\" \/>). when Th(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006216_inline2\" \/>) is unidimensional.<\/jats:p>","DOI":"10.2178\/jsl\/1146620159","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:22:51Z","timestamp":1198081371000},"page":"569-585","source":"Crossref","is-referenced-by-count":1,"title":["Morley degree in unidimensional compact complex spaces"],"prefix":"10.1017","volume":"71","author":[{"given":"Dale","family":"Radin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200006216_ref019","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/117"},{"key":"S0022481200006216_ref016","unstructured":"Radin D. , Unidimensional Zariski-type structures and applications to the model theory of compact complex spaces, Ph.D. thesis, University of Illinois at Chicago, 2004."},{"key":"S0022481200006216_ref014","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-03-03383-X"},{"key":"S0022481200006216_ref013","first-page":"737","volume":"67","author":"Pillay","year":"2002","journal-title":"Compact complex manifolds with the DOP and other properties"},{"key":"S0022481200006216_ref012","first-page":"1189","volume":"67","author":"Pillay","year":"2002","journal-title":"On Lascar rank and Morley rank of definable groups in differentially closed fields"},{"key":"S0022481200006216_ref010","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1201\/9781439865736-12","volume-title":"Logic colloquium '01","volume":"20","author":"Moosa","year":"2005"},{"key":"S0022481200006216_ref009","article-title":"On saturation and the model theory of compact K\u00e4hler manifolds","author":"Moosa","year":"2003","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"S0022481200006216_ref007","volume-title":"Seminaire F. Norguet, vol. 111","author":"Lieberman","year":"1978"},{"key":"S0022481200006216_ref006","volume-title":"Stability in model theory","volume":"36","author":"Lascar","year":"1987"},{"key":"S0022481200006216_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-96-00180-4"},{"key":"S0022481200006216_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808211"},{"key":"S0022481200006216_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09873-8"},{"key":"S0022481200006216_ref001","article-title":"Desingularization theorems","volume":"30","author":"Aroca","year":"1977","journal-title":"Memorias de Matem\u00e1tica del Instituto Jorge Juan, Madrid"},{"key":"S0022481200006216_ref015","first-page":"241","volume":"691","author":"Radin","year":"2004","journal-title":"A definability result for compact complex spaces"},{"key":"S0022481200006216_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/270\/04380"},{"key":"S0022481200006216_ref008","unstructured":"Moosa R. , Contributions to the model theory of fields and compact complex spaces, Ph.D. thesis. University of Illinois at Urbana-Champaign. 2001."},{"key":"S0022481200006216_ref018","unstructured":"Zilber B. , Lecture notes on Zariski-type structures. Delivered in the UIC logic seminar. Fall 1991."},{"key":"S0022481200006216_ref017","volume-title":"Classification theory (revised edition)","volume":"92","author":"Shelah","year":"1990"},{"key":"S0022481200006216_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69582-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200006216","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:54:08Z","timestamp":1630371248000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200006216\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,6]]}},"alternative-id":["S0022481200006216"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1146620159","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6]]}}}