{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T17:25:39Z","timestamp":1694625939425},"reference-count":5,"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":9873,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1987,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a countable complete <jats:italic>o<\/jats:italic>-minimal theory <jats:bold>T<\/jats:bold>, we introduce the notion of a sequentially complete model of <jats:bold>T<\/jats:bold>. We show that a model <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030073_inline4.png\" \/> of <jats:bold>T<\/jats:bold> is sequentially complete if and only if <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030073_inline4.png\" \/> \u227a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030073_inline1.png\" \/> for some Dedekind complete model <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030073_inline1.png\" \/>. We also prove that if <jats:bold>T<\/jats:bold> has a Dedekind complete model of power greater than <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030073_inline2.png\" \/>, then <jats:bold>T<\/jats:bold> has Dedekind complete models of arbitrarily large powers. Lastly, we show that a <jats:italic>dyadic theory<\/jats:italic>\u2014namely, a theory relative to which every formula is equivalent to a Boolean combination of formulas in two variables\u2014that has some Dedekind complete model has Dedekind complete models in arbitrarily large powers.<\/jats:p>","DOI":"10.2307\/2273870","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:20:33Z","timestamp":1146954033000},"page":"156-164","source":"Crossref","is-referenced-by-count":0,"title":["On Dedekind complete o-minimal structures"],"prefix":"10.1017","volume":"52","author":[{"given":"Anand","family":"Pillay","sequence":"first","affiliation":[]},{"given":"Charles","family":"Steinhorn","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200030073_bib004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0833697-X"},{"key":"S0022481200030073_bib002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0833698-1"},{"key":"S0022481200030073_bib005","volume-title":"Transactions of the American Mathematical Society","author":"Pillay"},{"key":"S0022481200030073_bib003","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1984-15249-2"},{"key":"S0022481200030073_bib001","first-page":"63","volume":"51","author":"Marker","year":"1986","journal-title":"Omitting types in \n                     \n                  -minimal theories"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200030073","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T08:14:15Z","timestamp":1649664855000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200030073\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,3]]},"references-count":5,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1987,3]]}},"alternative-id":["S0022481200030073"],"URL":"https:\/\/doi.org\/10.2307\/2273870","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,3]]}}}