{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:37:19Z","timestamp":1759639039313},"reference-count":12,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,5,11]],"date-time":"2006-05-11T00:00:00Z","timestamp":1147305600000},"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":[[2006,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper is a contribution to the development of model theory of fuzzy logic in narrow sense. We consider a formal system Ev<jats:sub>\u0141<\/jats:sub> of fuzzy logic that has evaluated syntax, i. e. axioms need not be fully convincing and so, they form a fuzzy set only. Consequently, formulas are provable in some general degree. A generalization of G\u00f6del's completeness theorem does hold in Ev<jats:sub>\u0141<\/jats:sub>. The truth values form an MV\u2010algebra that is either finite or \u0141ukasiewicz algebra on [0, 1].<\/jats:p><jats:p>The classical omitting types theorem states that given a formal theory <jats:italic>T<\/jats:italic> and a set \u03a3(<jats:italic>x<\/jats:italic> <jats:sub>1<\/jats:sub>, \u2026 , <jats:italic>x<jats:sub>n<\/jats:sub><\/jats:italic> ) of formulas with the same free variables, we can construct a model of <jats:italic>T<\/jats:italic> which omits \u03a3, i. e. there is always a formula from \u03a3 not true in it. In this paper, we generalize this theorem for Ev<jats:sub>\u0141<\/jats:sub>, that is, we prove that if <jats:italic>T<\/jats:italic> is a <jats:italic>fuzzy theory<\/jats:italic> and \u03a3(<jats:italic>x<\/jats:italic> <jats:sub>1<\/jats:sub>, \u2026 , <jats:italic>x<jats:sub>n<\/jats:sub><\/jats:italic> ) forms a <jats:italic>fuzzy set<\/jats:italic> , then a model omitting \u03a3 also exists. We will prove this theorem for two essential cases of Ev<jats:sub>\u0141<\/jats:sub>: either Ev<jats:sub>\u0141<\/jats:sub> has logical (truth) constants for all truth values, or it has these constants for truth values from [0, 1] \u2229 \u211a only. (\u00a9 2006 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200510031","type":"journal-article","created":{"date-parts":[[2006,5,11]],"date-time":"2006-05-11T11:57:25Z","timestamp":1147348645000},"page":"259-268","source":"Crossref","is-referenced-by-count":10,"title":["Omitting types in fuzzy logic with evaluated syntax"],"prefix":"10.1002","volume":"52","author":[{"given":"Petra","family":"Murinov\u00e1","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vil\u00e9m","family":"Nov\u00e1k","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,5,11]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"J. L.Bell andA. B.Slomson Models and Ultraproducts (North\u2010Holland Publishing Company 1969)."},{"key":"e_1_2_1_3_2","unstructured":"C. C.Chang andH. J.Keisler Model Theory (North\u2010Holland Publishing Company 1973)."},{"key":"e_1_2_1_4_2","unstructured":"S.Gottwald A Treatise on Many\u2010Valued Logics (Research Studies Press Ltd. 2001)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"P.H\u00e1jek Metamathematics of Fuzzy Logic (Kluwer 1998).","DOI":"10.1007\/978-94-011-5300-3"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1080\/0308107031000152522"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"A.Marcja andC.Toffalori A Guide to Classical and Modern Model Theory (Kluwer 2003).","DOI":"10.1007\/978-94-007-0812-9"},{"key":"e_1_2_1_8_2","unstructured":"P.Murinov\u00e1 andV.Nov\u00e1k Omitting types in fuzzy predicate logics. Submitted to Proc. of 26th Linz Seminar on Fuzzy Set Theory."},{"key":"e_1_2_1_9_2","unstructured":"V.Nov\u00e1k Fuzzy logic revisited. In: Proc. Int. Conference EUFIT'94 pp. 496\u2013499 (Verlag der Augustinus Buchhandlung 1994)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/1521-3870(200211)48:4<563::AID-MALQ563>3.0.CO;2-W"},{"key":"e_1_2_1_11_2","unstructured":"V.Nov\u00e1k Fuzzy logic with countable evaluated syntax. In: Fuzzy Logic Soft Computing and Computational Intelligence II. Eleventh IFSAWorld Congress pp. 1264\u20131269 (Tsinghua Univ. 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