{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T10:17:45Z","timestamp":1706091465519},"reference-count":12,"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":376,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that for a finitely generated infinite nilpotent group <jats:italic>G<\/jats:italic> with structure (<jats:italic>G<\/jats:italic>, \u00b7, \u2026), the connected component <jats:italic>G<\/jats:italic>*<jats:sup>0<\/jats:sup> of a sufficiently saturated extension <jats:italic>G<\/jats:italic>* of <jats:italic>G<\/jats:italic> exists and equals<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200000396_eqnU01\" \/><\/jats:disp-formula><\/jats:p><jats:p>We construct an expansion of \u2124 by a predicate (\u2124, +, <jats:italic>P<\/jats:italic>) such that the type-connected component <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000396_inline01\" \/> is strictly smaller than \u2124*<jats:sup>0<\/jats:sup>. We generalize this to finitely generated virtually solvable groups. As a corollary of our construction we obtain an optimality result for the van der Waerden theorem for finite partitions of groups.<\/jats:p>","DOI":"10.2178\/jsl.7801170","type":"journal-article","created":{"date-parts":[[2013,1,23]],"date-time":"2013-01-23T14:38:23Z","timestamp":1358951903000},"page":"245-259","source":"Crossref","is-referenced-by-count":2,"title":["Model theoretic connected components of finitely generated nilpotent groups"],"prefix":"10.1017","volume":"78","author":[{"given":"Nathan","family":"Bowler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakub","family":"Gismatullin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200000396_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9964-6"},{"key":"S0022481200000396_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-96-01456-0"},{"key":"S0022481200000396_ref005","volume-title":"Ramsey theory","author":"Graham","year":"1990"},{"key":"S0022481200000396_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-011-0067-8"},{"key":"S0022481200000396_ref002","unstructured":"Gismatullin J. , Absolute connectedness and classical groups, 2011, preprint, arXiv: 1002.1516."},{"key":"S0022481200000396_ref012","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061304000346"},{"key":"S0022481200000396_ref008","first-page":"49","article-title":"On homomorphisms onto finite groups","volume":"18","author":"Mal'cev","year":"1958","journal-title":"Uchenye zapiski Ivanovslcogo pedagogicheskogo instituta"},{"key":"S0022481200000396_ref011","first-page":"1783","volume":"66","author":"Miller","year":"2001","journal-title":"Expansions of dense linear orders with the intermediate value property"},{"key":"S0022481200000396_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-008-0092-4"},{"key":"S0022481200000396_ref009","volume-title":"Model theory","volume":"217","author":"Marker","year":"2002"},{"key":"S0022481200000396_ref001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061301000119"},{"key":"S0022481200000396_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1994-1264149-8"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000396","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T19:12:16Z","timestamp":1556133136000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000396\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["S0022481200000396"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7801170","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3]]}}}