{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T19:59:29Z","timestamp":1694116769652},"reference-count":9,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T00:00:00Z","timestamp":1490918400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p>Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600029-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600029:malq201600029-math-0001\" \/> be a weakly o\u2010minimal structure with the strong cell decomposition property. In this note, we show that the canonical o\u2010minimal extension <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600029-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600029:malq201600029-math-0002\" \/> of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600029-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600029:malq201600029-math-0003\" \/> is the unique prime model of the full first order theory of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600029-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600029:malq201600029-math-0004\" \/> over any set <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600029-math-0005.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600029:malq201600029-math-0005\" \/>. We also show that if two weakly o\u2010minimal structures with the strong cell decomposition property are isomorphic then, their canonical o\u2010minimal extensions are isomorphic too. Finally, we show the uniqueness of the prime models in a complete weakly o\u2010minimal theory with prime models.<\/jats:p>","DOI":"10.1002\/malq.201600029","type":"journal-article","created":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T15:15:07Z","timestamp":1490973307000},"page":"109-113","source":"Crossref","is-referenced-by-count":1,"title":["A note on prime models in weakly o\u2010minimal structures"],"prefix":"10.1002","volume":"63","author":[{"given":"Somayyeh","family":"Tari","sequence":"first","affiliation":[{"name":"Department of Mathematics Azarbaijan Shahid Madani University Kilometer 35, Tabriz\/Azarshahr Road Tabriz 53714\u2010161 Islamic Republic of Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2017,3,31]]},"reference":[{"key":"e_1_2_5_2_1","first-page":"570","article-title":"Expansion of a model of weakly o\u2010minimal theory by family of unary predicates","volume":"63","author":"Baizhanov B. S.","year":"1998","journal-title":"J. Symb. 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