{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T05:40:18Z","timestamp":1698385218874},"reference-count":18,"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":3969,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1996,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We provide results allowing to state, by the simple inspection of suitable classes of posets (propositional Kripke frames), that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2<jats:sup>No<\/jats:sup> maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property.<\/jats:p><jats:p>Mathematics Subject Classification: 03B55, 03C90.<\/jats:p>","DOI":"10.1002\/malq.19960420141","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T15:34:48Z","timestamp":1180539288000},"page":"501-536","source":"Crossref","is-referenced-by-count":0,"title":["Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property"],"prefix":"10.1002","volume":"42","author":[{"given":"Guido","family":"Bertolotti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierangelo","family":"Miglioli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniela","family":"Silvestrini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274513"},{"key":"e_1_2_1_3_2","first-page":"117","article-title":"The cardinality of the set of maximal itermediate logics with the disjunction property is of continuum","volume":"51","author":"Chagrov A. V.","year":"1992","journal-title":"Mat. Zametki"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370182"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275149"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00053-6"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00052-5"},{"key":"e_1_2_1_8_2","unstructured":"Galanter G. I. A continuum of intermediate logics which are maximal among the logics having the intuitionistic disjunctionless fragment. In: Proceedings 10th USSR Conference for Mathematical Logic Alma Ata1990 p.41(in Russian)."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093883567"},{"key":"e_1_2_1_10_2","first-page":"288","article-title":"Some syntactic theorems on the calculus of finite problems of Ju","volume":"10","author":"Levin L. A.","year":"1969","journal-title":"T. Medvedev. Soviet Math. Dokl."},{"key":"e_1_2_1_11_2","unstructured":"Maksimova L. L. The number of maximal intermediate logics with the disjunction property. In: Proceedings 7th All\u2010Union Conference for Mathematical Logic Novosibirsk1984 pp.000\u2013000( in Russian)."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01881550"},{"key":"e_1_2_1_13_2","first-page":"227","article-title":"Finite problems","volume":"3","author":"Medvedev Ju. T.","year":"1962","journal-title":"Soviet Math. Dokl."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01277484"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093635238"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066744"},{"key":"e_1_2_1_17_2","first-page":"985","article-title":"On incomplete propositional logics","volume":"18","author":"\u0160hethman V. B.","year":"1977","journal-title":"Soviet Math. Dokl."},{"key":"e_1_2_1_18_2","first-page":"1288","article-title":"Rieger\u2010Nishimura lattices","volume":"241","author":"\u0160hethman V. B.","year":"1978","journal-title":"Doklady Acad. Nauk. SSSR"},{"key":"e_1_2_1_19_2","unstructured":"\u0160hethman V. B. Applications of Kripke Semantics to Studies in Modal and Intermediate Logics. PhD Thesis Moscow State University Moscow1984(in Russian)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19960420141","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19960420141","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T22:11:09Z","timestamp":1698358269000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19960420141"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["10.1002\/malq.19960420141"],"URL":"https:\/\/doi.org\/10.1002\/malq.19960420141","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,1]]}}}