{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,24]],"date-time":"2024-02-24T04:10:03Z","timestamp":1708747803506},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2293,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2007,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An amalgamation base<jats:italic>p<\/jats:italic>in a simple theory is<jats:italic>stably definable<\/jats:italic>if its canonical base is interde-finable with the set of canonical parameters for the \u03d5-definitions of<jats:italic>p<\/jats:italic>as \u03d5 ranges through all stable formulae. A necessary condition for stably definability is given and used to produce an example of a supersimple theory with stable forking having types that are not stably definable. This answers negatively a question posed in [8]. A criterion for and example of a stably definable amalgamation base whose restriction to the canonical base is not axiomatised by stable formulae are also given. The examples involve generic relations over non CM-trivial stable theories.<\/jats:p>","DOI":"10.2178\/jsl\/1203350778","type":"journal-article","created":{"date-parts":[[2008,3,25]],"date-time":"2008-03-25T18:42:11Z","timestamp":1206470531000},"page":"1163-1176","source":"Crossref","is-referenced-by-count":0,"title":["Stable definability and generic relations"],"prefix":"10.1017","volume":"72","author":[{"given":"Byunghan","family":"Kim","sequence":"first","affiliation":[]},{"given":"Rahim","family":"Moosa","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200004837_ref009","first-page":"474","volume":"65","author":"Pillay","year":"2000","journal-title":"A note on CM-triviality and the geometry of forking"},{"key":"S0022481200004837_ref007","first-page":"293","volume":"65","author":"Kim","year":"2000","journal-title":"Coordinatisation and canonical bases in simple theories"},{"key":"S0022481200004837_ref006","first-page":"822","volume":"66","author":"Kim","year":"2001","journal-title":"Simplicity, and stability in there"},{"key":"S0022481200004837_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0090164"},{"key":"S0022481200004837_ref001","first-page":"443","volume":"65","author":"Baudisch","year":"2000","journal-title":"A free pseudospace"},{"key":"S0022481200004837_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90171-9"},{"key":"S0022481200004837_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(98)00021-9"},{"key":"S0022481200004837_ref008","doi-asserted-by":"publisher","DOI":"10.4064\/fm170-1-6"},{"key":"S0022481200004837_ref010","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1093\/oso\/9780198534686.003.0006","volume-title":"Automorphisms of first-order structures","author":"Wagner","year":"1994"},{"key":"S0022481200004837_ref005","first-page":"151","volume-title":"Model theory and applications","volume":"11","author":"Hrushovski","year":"2005"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200004837","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,24]],"date-time":"2024-02-24T03:44:57Z","timestamp":1708746297000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200004837\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,12]]}},"alternative-id":["S0022481200004837"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1203350778","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12]]}}}