{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:17Z","timestamp":1761611177978},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":7406,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1993,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A proof is given that the set of maximal intermediate propositional logics with the disjunction property and the set of maximal intermediate predicate logics with the disjunction property and the explicit definability property have the power of continuum. To prove our results, we introduce various notions which might be interesting by themselves. In particular, we illustrate a method to generate wide sets of pairwise \u201cconstructively incompatible constructive logics\u201d. We use a notion of \u201csemiconstructive\u201d logic and define wide sets of \u201cconstructive\u201d logics by representing the \u201cconstructive\u201d logics as \u201climits\u201d of decreasing sequences of \u201csemiconstructive\u201d logics. Also, we introduce some generalizations of the usual filtration techniques for propositional logics. For instance, \u201cfitrations over rank formulas\u201d are used to show that any two different logics belonging to a suitable uncountable set of \u201cconstructive\u201d logics are \u201cconstructively incompatible\u201d.<\/jats:p>","DOI":"10.2307\/2275149","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:50:13Z","timestamp":1146955813000},"page":"1365-1401","source":"Crossref","is-referenced-by-count":16,"title":["Counting the maximal intermediate constructive logics"],"prefix":"10.1017","volume":"58","author":[{"given":"Mauro","family":"Ferrari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierangelo","family":"Miglioli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120002065X_ref026","first-page":"35","article-title":"Intermediate logics with the disjunction property","volume":"1","author":"Wronski","year":"1973","journal-title":"Reports on Mathematical Logic"},{"key":"S002248120002065X_ref025","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066744"},{"key":"S002248120002065X_ref024","unstructured":"Shehtman V. B. , Applications of Kripke models to studies in modal and intermediate logic, Ph.D. Thesis, Moscow State University, Moscow, 1984. (Russian)"},{"key":"S002248120002065X_ref022","doi-asserted-by":"publisher","DOI":"10.1111\/j.1755-2567.1968.tb00337.x"},{"key":"S002248120002065X_ref020","first-page":"55","article-title":"Some problems on intermediate predicate logics","volume":"21","author":"Ono","year":"1987","journal-title":"Reports on Mathematical Logic"},{"key":"S002248120002065X_ref019","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195192964"},{"key":"S002248120002065X_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BF01277484"},{"key":"S002248120002065X_ref003","volume-title":"The ITLI prepuhlication series","author":"Chagrov","year":"1991"},{"key":"S002248120002065X_ref001","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19720180802"},{"key":"S002248120002065X_ref006","first-page":"431","volume":"35","author":"Gabbay","year":"1970","journal-title":"The decidability of the Kreisel-Putnam system"},{"key":"S002248120002065X_ref021","first-page":"440","article-title":"Admissible rules of pretabular modal logics","volume":"20","author":"Rybakov","year":"1981","journal-title":"Algehra i Logika"},{"key":"S002248120002065X_ref017","volume-title":"Indagini semantiche sulle logiche intermedie proposizionali","author":"Minari","year":"1989"},{"key":"S002248120002065X_ref002","first-page":"117","article-title":"The cardinality of the set of maximal intermediate logics with the disjunction property is of continuum","volume":"51","author":"Chagrov","year":"1992","journal-title":"Matematicheskie Zametki"},{"key":"S002248120002065X_ref009","first-page":"41","volume-title":"Proceedings of 10th USSR Conference for Mathematical Logic","author":"Galanter","year":"1990"},{"key":"S002248120002065X_ref023","first-page":"1288","article-title":"Rieger-Nishimura lattices","volume":"241","author":"Shehtman","year":"1978","journal-title":"Doklady AN SSSR"},{"key":"S002248120002065X_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2977-2"},{"key":"S002248120002065X_ref005","first-page":"619","volume":"50","author":"Fine","year":"1985","journal-title":"Logics containing K4, part II"},{"key":"S002248120002065X_ref004","unstructured":"Doets K. , Definability in intensional and high order logic, Ph.D. Thesis, University of Amsterdam, Amsterdam, 1986."},{"key":"S002248120002065X_ref008","first-page":"67","volume":"39","author":"Gabbay","year":"1974","journal-title":"A sequence of decidable finitely axiomatizable intermediate logics with the disjunction property"},{"key":"S002248120002065X_ref010","first-page":"806","article-title":"Constructing a sequence of strongly independent superintuilionistic propositional calculi","volume":"9","author":"Jankov","year":"1968","journal-title":"Soviet Mathematics-Doklady"},{"key":"S002248120002065X_ref018","first-page":"859","volume-title":"Proceedings of the Japan Academy","volume":"42","author":"Nagata","year":"1966"},{"key":"S002248120002065X_ref011","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093883567"},{"key":"S002248120002065X_ref012","unstructured":"Kracht M. , Intensional definability and completeness in modal logic, Ph.D. Thesis, Freie Universit\u00e4t, Berlin, 1990."},{"key":"S002248120002065X_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/BF01988049"},{"key":"S002248120002065X_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF01881550"},{"key":"S002248120002065X_ref015","volume-title":"Proceedings of the 7th All-Union Conference for Mathematical Logic","author":"Maksimova","year":"1984"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120002065X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T21:03:32Z","timestamp":1557954212000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120002065X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,12]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1993,12]]}},"alternative-id":["S002248120002065X"],"URL":"https:\/\/doi.org\/10.2307\/2275149","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,12]]}}}