{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:08:42Z","timestamp":1760202522120},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8593,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,9]]},"abstract":"Abstract<\/jats:title>For each ordinal \u03b1<\/jats:italic> > 0, L<\/jats:italic>(\u03b1<\/jats:italic>) is the intermediate predicate logic characterized by the class of all Kripke frames with the poset \u03b1<\/jats:italic> and with constant domain. This paper will be devoted to a study of logics of the form L<\/jats:italic>(\u03b1<\/jats:italic>). It will be shown that for each uncountable ordinal of the form \u03b1<\/jats:italic> + \u03b7<\/jats:italic> with a finite or a countable \u03b7<\/jats:italic>(><\/jats:italic> 0), there exists a countable ordinal of the form \u03b2<\/jats:italic> + \u03b7<\/jats:italic> such that L<\/jats:italic>(\u03b1<\/jats:italic> + \u03b7<\/jats:italic>) = L<\/jats:italic>(\u03b2<\/jats:italic> + \u03b7<\/jats:italic>). On the other hand, such a reduction of ordinals to countable ones is impossible for a logic L<\/jats:italic>(\u03b1<\/jats:italic>) if \u03b1<\/jats:italic> is an uncountable regular ordinal. Moreover, it will be proved that the mapping L<\/jats:italic> is injective if it is restricted to ordinals less than \u03c9\u03c9<\/jats:sup><\/jats:italic>, i.e. \u03b1<\/jats:italic> \u2260 \u03b2<\/jats:italic> implies L<\/jats:italic>(\u03b1<\/jats:italic>) \u2260 L<\/jats:italic>(\u03b2<\/jats:italic>) for each ordinal \u03b1, \u03b2<\/jats:italic> \u2264 \u03c9\u03c9<\/jats:sup><\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2274476","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:36:50Z","timestamp":1146940610000},"page":"1099-1124","source":"Crossref","is-referenced-by-count":7,"title":["Intermediate predicate logics determined by ordinals"],"prefix":"10.1017","volume":"55","author":[{"given":"Pierluigi","family":"Minari","sequence":"first","affiliation":[]},{"given":"Mitio","family":"Takano","sequence":"additional","affiliation":[]},{"given":"Hiroakira","family":"Ono","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025585_ref015","first-page":"69","article-title":"A negative answer to Ono's first problem: K-completeness does not imply strong K-completeness","volume":"21","author":"Takano","year":"1987","journal-title":"Reports on Mathematical Logic"},{"key":"S0022481200025585_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370376"},{"key":"S0022481200025585_ref012","first-page":"287","volume-title":"Studies in nonclassical logics and formal systems","author":"Shehtman","year":"1983"},{"key":"S0022481200025585_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF00671568"},{"key":"S0022481200025585_ref009","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195192964"},{"key":"S0022481200025585_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02308-2"},{"key":"S0022481200025585_ref005","first-page":"67","article-title":"Intermediate propositional logics (a survey)","volume":"5","author":"Hosoi","year":"1973","journal-title":"Journal of Tsuda College"},{"key":"S0022481200025585_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-5203-4_4"},{"key":"S0022481200025585_ref001","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093634994"},{"key":"S0022481200025585_ref007","first-page":"185","article-title":"Kripke-definable ordinals","volume":"2","author":"Minari","year":"1985","journal-title":"Atti degli incontri di logica matematica, Universit\u00e0 di Siena"},{"key":"S0022481200025585_ref008","unstructured":"Minari P. , A strong L\u00f6wenheim-Skolem-type theorem for Kripke semantic, unpublished."},{"key":"S0022481200025585_ref002","first-page":"243","volume-title":"Atti degli incontri di logica matematica 1982","author":"Casari","year":"1983"},{"key":"S0022481200025585_ref010","first-page":"55","article-title":"Some problems in intermediate predicate logics","volume":"21","author":"Ono","year":"1987","journal-title":"Reports on Mathematical Logic"},{"key":"S0022481200025585_ref013","first-page":"115","article-title":"On axiomatizability of some intermediate predicate logics","volume":"22","author":"Skvortsov","year":"1988","journal-title":"Reports on Mathematical Logic"},{"key":"S0022481200025585_ref003","first-page":"80","volume-title":"Complexity problems in mathematical logic","author":"Chagrov","year":"1985"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025585","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T16:24:53Z","timestamp":1558196693000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025585\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1990,9]]}},"alternative-id":["S0022481200025585"],"URL":"https:\/\/doi.org\/10.2307\/2274476","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}