{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,17]],"date-time":"2025-01-17T05:21:41Z","timestamp":1737091301057,"version":"3.33.0"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We define a property for varieties V, the<jats:italic>f.r.p.<\/jats:italic>(<jats:italic>finite replacement property<\/jats:italic>). If it applies to a finitely based V then V is strongly finitely based in the sense of [14], see Theorem 2. Moreover, we obtain finite axiomatizability results for certain propositional logics associated with V, in its generality comparable to well\u2010known finite base results from equational logic. Theorem 3 states that each variety generated by a 2\u2010element algebra has the<jats:italic>f.r.p.<\/jats:italic>Essentially this implies finite axiomatizability of a 2\u2010valued logic in<jats:italic>any finite<\/jats:italic>language.<\/jats:p>","DOI":"10.1002\/malq.19920380131","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T00:45:25Z","timestamp":1180399525000},"page":"327-344","source":"Crossref","is-referenced-by-count":3,"title":["FINITE REPLACEMENT AND FINITE HILBERT\u2010STYLE AXIOMATIZABILITY"],"prefix":"10.1002","volume":"38","author":[{"given":"B.","family":"Herrmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"W.","family":"Rautenberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"volume-title":"Distributive Lattices","year":"1974","author":"Balbes R.","key":"e_1_2_1_2_2"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"Blok W. J.andD.Pigozzi Algebraizable Logics. Memoirs of the AMS396(1989).","DOI":"10.1090\/memo\/0396"},{"key":"e_1_2_1_4_2","first-page":"497","article-title":"Zur Logik der Modalit\u00e4ten","author":"Becker O.","year":"1930","journal-title":"Jahrbuch Phil. u. Ph\u00e4nom."},{"key":"e_1_2_1_5_2","first-page":"142","article-title":"A proof of Lyndon's finite base theorem","volume":"9","author":"Berman J.","year":"1979","journal-title":"Alg. Univ."},{"key":"e_1_2_1_6_2","unstructured":"Berman J. Algebraic Properties ofk\u2010valued Logics. Proc. 10. Int. Symp. Multiplevalued Logic Evanston1980."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370368"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/1990703"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(69)90058-1"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","unstructured":"Post E. Two\u2010valued Iterative Systems of Mathematical Logic. 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Discriminator\u2010Algebras Berlin1978.","DOI":"10.1515\/9783112733332"},{"key":"e_1_2_1_19_2","doi-asserted-by":"crossref","unstructured":"W\u00f3jcicki R. Theory of Logical Calculi. Dordrecht1988.","DOI":"10.1007\/978-94-015-6942-2"},{"key":"e_1_2_1_20_2","first-page":"68","article-title":"A 3\u2010valued matrix whose consequence operation is not finitely based","volume":"8","author":"Wro\u0144ski A.","year":"1979","journal-title":"Bull. Sec. Logic"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380131","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T18:47:48Z","timestamp":1737053268000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380131"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380131","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}