{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:19:48Z","timestamp":1759033188682},"reference-count":14,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2008,7,10]],"date-time":"2008-07-10T00:00:00Z","timestamp":1215648000000},"content-version":"vor","delay-in-days":9,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2008,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In [10] it is claimed that the set of predicate tautologies of all complete BL\u2010chains and the set of all standard tautologies (i. e., the set of predicate formulas valid in all standard BL\u2010algebras) coincide. As noticed in [11], this claim is wrong. In this paper we show that a complete BL\u2010chain <jats:bold><jats:italic>B<\/jats:italic><\/jats:bold> satisfies all standard BL\u2010tautologies iff for any transfinite sequence (<jats:italic>a<jats:sub>i<\/jats:sub><\/jats:italic>: <jats:italic>i<\/jats:italic> \u2208 <jats:italic>I<\/jats:italic>) of elements of <jats:bold><jats:italic>B<\/jats:italic><\/jats:bold>, the condition \u2227<jats:sub><jats:italic>i<\/jats:italic> \u2208 <jats:italic>I<\/jats:italic> <\/jats:sub> (<jats:italic>a<\/jats:italic><jats:sup>2<\/jats:sup><jats:sub><jats:italic>i<\/jats:italic> <\/jats:sub>) = (\u2227<jats:sub><jats:italic>i<\/jats:italic> \u2208 <jats:italic>I<\/jats:italic> <\/jats:sub> <jats:italic>a<jats:sub>i<\/jats:sub><\/jats:italic>)<jats:sup>2<\/jats:sup> holds in <jats:bold><jats:italic>B<\/jats:italic><\/jats:bold>. (\u00a9 2008 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710058","type":"journal-article","created":{"date-parts":[[2008,7,10]],"date-time":"2008-07-10T09:52:45Z","timestamp":1215683565000},"page":"435-446","source":"Crossref","is-referenced-by-count":14,"title":["A note on the first\u2010order logic of complete BL\u2010chains"],"prefix":"10.1002","volume":"54","author":[{"given":"Petr","family":"H\u00e1jek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Franco","family":"Montagna","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2008,7,10]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(02)00329-8"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"A.Glass Partially Ordered Groups. 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E.Ragaz Arithmetische Klassifikation von Formelmengen der unendlichwertigen Logik. Ph. D. thesis ETH Z\u00fcrich (1981)."},{"key":"e_1_2_1_15_2","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1090\/S0002-9947-1939-1501995-3","article-title":"Residuated lattices","volume":"45","author":"Ward M.","year":"1939","journal-title":"Trans. Amer. Math. Soc."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710058","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200710058","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T13:50:33Z","timestamp":1699969833000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200710058"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["10.1002\/malq.200710058"],"URL":"https:\/\/doi.org\/10.1002\/malq.200710058","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7]]}}}