{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T09:47:25Z","timestamp":1775814445314,"version":"3.50.1"},"reference-count":8,"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":7224,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1994,6]]},"abstract":"<jats:p>We know from [H1], [H2] that in a stable theory, given a nontrivial locally modular regular type <jats:italic>q<\/jats:italic>, one can define a group with generic domination equivalent to <jats:italic>q<\/jats:italic>, and that the dependence relation on <jats:italic>q<\/jats:italic> can be analyzed in terms of this group. In a stable one-based theory, every regular type is locally modular; hence, this result holds for every nontrivial regular type. We show here that, in fact, in a stable one-based theory, a similar type of construction can be done without the assumption of regularity. More precisely, we show that for any type <jats:italic>q<\/jats:italic>, the nontrivial part of <jats:italic>q<\/jats:italic> can be analyzed by generics of groups and that any nontrivial relation can be described by affine relations (Theorem A).<\/jats:p><jats:p>This construction is then used to answer a question about homogeneity in pairs of models which is still open in the case of arbitrary stable theories (Theorem C).<\/jats:p>","DOI":"10.2307\/2275409","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:51:53Z","timestamp":1146941513000},"page":"579-595","source":"Crossref","is-referenced-by-count":7,"title":["On one-based theories"],"prefix":"10.1017","volume":"59","author":[{"given":"E.","family":"Bouscaren","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"Hrushovski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120001999X_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600562"},{"key":"S002248120001999X_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(80)90002-0"},{"key":"S002248120001999X_ref003","volume-title":"Abelian groups theory, 2nd New Mexico State University Conference 1976","volume":"616","author":"Fisher"},{"key":"S002248120001999X_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90001-8"},{"key":"S002248120001999X_ref001","volume-title":"The model theory of groups (1989)","volume":"11","author":"Bouscaren","year":"1989"},{"key":"S002248120001999X_ref005","volume-title":"Classification theory: Chicago 1985","author":"Hrushovski","year":"1987"},{"key":"S002248120001999X_ref006","volume-title":"Proceedings of Logic Colloquium '85","author":"Hrushovski","year":"1986"},{"key":"S002248120001999X_ref004","unstructured":"Hrushovski E. , Contributions to model theory, Ph.D. thesis , University of California at Berkeley, Berkeley, California, 1986."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120001999X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T00:00:02Z","timestamp":1557878402000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120001999X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,6]]}},"alternative-id":["S002248120001999X"],"URL":"https:\/\/doi.org\/10.2307\/2275409","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,6]]}}}