{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T09:41:27Z","timestamp":1775209287464,"version":"3.50.1"},"reference-count":22,"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>Generalising Hrushovski's fusion technique we construct the free fusion of two strongly minimal theories<jats:italic>T<\/jats:italic><jats:sub>1<\/jats:sub>.<jats:italic>T<\/jats:italic><jats:sub>2<\/jats:sub>intersecting in a totally categorical sub-theory<jats:italic>T<\/jats:italic><jats:sub>0<\/jats:sub>. We show that if. e.g.,<jats:italic>T<\/jats:italic><jats:sub>0<\/jats:sub>is the theory of infinite vector spaces over a finite field then the fusion theory<jats:italic>T<\/jats:italic><jats:sub>\u03c9<\/jats:sub>, exists, is complete and \u03c9-stable of rank \u03c9. We give a detailed geometrical analysis of<jats:italic>T<\/jats:italic><jats:sub>\u03c9<\/jats:sub>, proving that if both<jats:italic>T<\/jats:italic><jats:sub>1<\/jats:sub>,<jats:italic>T<\/jats:italic><jats:sub>2<\/jats:sub>are 1-based then.<jats:italic>T<\/jats:italic>\u03c9 can be collapsed into a strongly minimal theory, if some additional technical conditions hold\u2014all trivially satisfied if<jats:italic>T<\/jats:italic><jats:sub>0<\/jats:sub>is the theory of infinite vector spaces over a finite field<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006113_inline1\"\/>.<\/jats:p>","DOI":"10.2178\/jsl\/1146620149","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:22:51Z","timestamp":1198081371000},"page":"361-398","source":"Crossref","is-referenced-by-count":4,"title":["Fusion over sublanguages"],"prefix":"10.1017","volume":"71","author":[{"given":"Assaf","family":"Hasson","sequence":"first","affiliation":[]},{"given":"Martin","family":"Hils","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200006113_ref012","unstructured":"Hasson A. . Collapsing structure and a theory of envelopes, preprint. 2004."},{"key":"S0022481200006113_ref020","first-page":"1339","volume":"64","author":"Poizat","year":"1999","journal-title":"Le carr\u00e9 de l'\u00e9galit\u00e9"},{"key":"S0022481200006113_ref022","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/117"},{"key":"S0022481200006113_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2003.10.003"},{"key":"S0022481200006113_ref016","first-page":"946","volume":"64","author":"Holland","year":"1999","journal-title":"Model completeness of the new strongly minimal sets"},{"key":"S0022481200006113_ref007","doi-asserted-by":"crossref","unstructured":"Baudisch A. , Martin-Pizarro A. , and Ziegler M. , Fusion over a vector space, preprint. 2005.","DOI":"10.1142\/S0219061306000542"},{"key":"S0022481200006113_ref015","unstructured":"Hils M. , Ph.D. thesis, in preperation."},{"key":"S0022481200006113_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07330-8"},{"key":"S0022481200006113_ref021","first-page":"1647","volume":"66","author":"Poizat","year":"2001","journal-title":"L'\u00e9galit\u00e9 au cube"},{"key":"S0022481200006113_ref002","doi-asserted-by":"crossref","unstructured":"Baldwin J. 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(Available on author's webpage)."},{"key":"S0022481200006113_ref010","volume-title":"Skew field constructions","volume":"27","author":"Cohn","year":"1977"},{"key":"S0022481200006113_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90171-9"},{"key":"S0022481200006113_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808211"},{"key":"S0022481200006113_ref003","first-page":"371","volume":"65","author":"Baldwin","year":"2000","journal-title":"Constructing \u03c9-stable structures: Rank 2 fields"},{"key":"S0022481200006113_ref011","first-page":"670","volume":"55","author":"Gute","year":"1990","journal-title":"The last word on elimination of quantifiers in modules"},{"key":"S0022481200006113_ref004","doi-asserted-by":"publisher","DOI":"10.4064\/fm170-1-1"},{"key":"S0022481200006113_ref006","doi-asserted-by":"crossref","unstructured":"Baudisch A. , Martin-Pizarro A. , and Ziegler M. , Fields and colors, preprint. 2005.","DOI":"10.1007\/s10469-006-0008-5"},{"key":"S0022481200006113_ref009","volume-title":"Finite structures with few types","volume":"152","author":"Cherlin","year":"2003"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200006113","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T15:40:34Z","timestamp":1708443634000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200006113\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,6]]}},"alternative-id":["S0022481200006113"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1146620149","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6]]}}}