{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T05:16:14Z","timestamp":1697692574840},"reference-count":11,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2003,2,27]],"date-time":"2003-02-27T00:00:00Z","timestamp":1046304000000},"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":[[2003,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We describe the countably saturated models and prime models (up to isomorphism) of the theory Th<jats:sub>prin<\/jats:sub> of Boolean algebras with a principal ideal, the theory Th<jats:sub>max<\/jats:sub> of Boolean algebras with a maximal ideal, the theory Th<jats:sub>ac<\/jats:sub> of atomic Boolean algebras with an ideal such that the supremum of the ideal exists, and the theory Th<jats:sub>sa<\/jats:sub> of atomless Boolean algebras with an ideal such that the supremum of the ideal exists. We prove that there are infinitely many completions of the theory of Boolean algebras with a distinguished ideal that do not have a countably saturated model. Also, we give a sufficient condition for a model of the theory <jats:italic>T<\/jats:italic><jats:sub><jats:italic>X<\/jats:italic><\/jats:sub> of Boolean algebras with distinguished ideals to be elementarily equivalent to a countably saturated model of <jats:italic>T<\/jats:italic><jats:sub><jats:italic>X<\/jats:italic><\/jats:sub>.<\/jats:p>","DOI":"10.1002\/malq.200310026","type":"journal-article","created":{"date-parts":[[2003,3,18]],"date-time":"2003-03-18T23:12:20Z","timestamp":1048029140000},"page":"260-276","source":"Crossref","is-referenced-by-count":0,"title":["Some Boolean algebras with finitely many distinguished ideals II"],"prefix":"10.1002","volume":"49","author":[{"given":"Regina","family":"Arag\u00f3n","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2003,2,27]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19950410406"},{"key":"e_1_2_1_3_2","unstructured":"C. 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Amsterdam 1989)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","first-page":"25","DOI":"10.4064\/cm-41-1-25-33","article-title":"Recursive prime models for Boolean algebras","volume":"41","author":"Mead J.","year":"1979","journal-title":"Colloq. 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