{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T05:41:47Z","timestamp":1696570907460},"reference-count":9,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2013,12,20]],"date-time":"2013-12-20T00:00:00Z","timestamp":1387497600000},"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":[[2014,2]]},"abstract":"<jats:p>Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0001\" \/> denote a first\u2010order logic in a language that contains infinitely many constant symbols and also containing intuitionistic logic <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0002\" \/>. By <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0003\" \/>, we mean the associated logic axiomatized by the double negation of the universal closure of the axioms of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0004\" \/> plus <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0005.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0005\" \/>. We shall show that if <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0006.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0006\" \/> is <jats:italic>strongly complete<\/jats:italic> for a class of Kripke models <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0007.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0007\" \/>, then <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0008.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0008\" \/> is strongly complete for the class of Kripke models that are <jats:italic>ultimately<\/jats:italic> in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200083-math-0009.png\" xlink:title=\"urn:x-wiley:09425616:malq201200083:equation:malq201200083-math-0009\" \/>.<\/jats:p>","DOI":"10.1002\/malq.201200083","type":"journal-article","created":{"date-parts":[[2013,12,20]],"date-time":"2013-12-20T19:05:16Z","timestamp":1387566316000},"page":"6-11","source":"Crossref","is-referenced-by-count":0,"title":["Completeness of intermediate logics with doubly negated axioms"],"prefix":"10.1002","volume":"60","author":[{"given":"Mohammad","family":"Ardeshir","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences Sharif University of Technology, Azadi Ave  14588\u201089694 Tehran Iran"}]},{"given":"S. Mojtaba","family":"Mojtahedi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences Sharif University of Technology, Azadi Ave  14588\u201089694 Tehran Iran"}]}],"member":"311","published-online":{"date-parts":[[2013,12,20]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(03)00058-7"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370118"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01630811"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.2307\/2272556"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2977-2"},{"key":"e_1_2_6_7_1","volume-title":"Quantification in Nonclassical Logic, Studies in Logic and the Foundations of Mathematics","author":"Gabbay D.\u00a0M.","year":"2009"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2270260"},{"key":"e_1_2_6_9_1","volume-title":"Constructivism in Mathematics, Volume I: An Introduction, Studies in Logic and the Foundations of Mathematics","author":"Troelstra A. 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