{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T05:37:17Z","timestamp":1738129037163,"version":"3.33.0"},"reference-count":9,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T00:00:00Z","timestamp":1700179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,2,27]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We show that both the $n$-density and the bounded $n$-width of Kripke frames can be modally defined not only with natural and well-known Sahlqvist formulae containing a linear number of different propositional variables but also with formulae of polynomial length with a logarithmic number of different propositional variables and then we prove that this exponential decrease in the number of variables leads us outside the class of Sahlqvist formulae.<\/jats:p>","DOI":"10.1093\/jigpal\/jzad026","type":"journal-article","created":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T01:01:45Z","timestamp":1700442105000},"page":"95-124","source":"Crossref","is-referenced-by-count":0,"title":["On the number of different variables required to define the <i>n<\/i>-density or the bounded <i>n<\/i>-width of Kripke frames with some consequences for Sahlqvist formulae"],"prefix":"10.1093","volume":"33","author":[{"given":"Petar","family":"Iliev","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Informatics and Institute of Philosophy and Sociology , Bulgarian Academy of Sciences, Sofia, 1000, Bulgaria, petar.iliev@math.bas.bg"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,11,17]]},"reference":[{"volume-title":"Combinatorics of Finite Sets","year":"2002","author":"Anderson","key":"2025012810511243100_ref1"},{"key":"2025012810511243100_ref2","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1093\/jigpal\/jzaa068","article-title":"Frame-validity games and lower bounds on the complexity of modal axioms","volume":"30","author":"Balbiani","year":"2022","journal-title":"Logic Journal of the IGPL"},{"volume-title":"Modal Logic","year":"2010","author":"Blackburn","key":"2025012810511243100_ref3"},{"key":"2025012810511243100_ref4","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537793.001.0001","volume-title":"Modal Logic","author":"Chagrov","year":"1997"},{"key":"2025012810511243100_ref5","first-page":"77","article-title":"On canonical modal logics that are not elementarily determined","volume":"46","author":"Goldblatt","year":"2003","journal-title":"Logique et Analyse Nouvelle S\u00e9rie"},{"key":"2025012810511243100_ref6","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1093\/jigpal\/jzac044","article-title":"On semantically labelled syntax trees and the non-existence of certain Sahlqvist formulae","volume":"31","author":"Iliev","year":"2022","journal-title":"Logic Journal of the IGPL"},{"key":"2025012810511243100_ref7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-2566-9_8","article-title":"On proving lower bounds for circuit size","volume-title":"Feasible Mathematics II","author":"Karchmer","year":"1995"},{"volume-title":"An Essay in Classical Modal Logic","year":"1971","author":"Segerberg","key":"2025012810511243100_ref8"},{"key":"2025012810511243100_ref9","first-page":"499","article-title":"Modal definability in languages with a finite number of propositional variables and a new extension of the Sahlqvist\u2019s class","volume-title":"Proceedings of Advances in Modal Logic","author":"Vakarelov","year":"2003"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/33\/1\/95\/53485524\/jzad026.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/33\/1\/95\/53485524\/jzad026.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T10:51:24Z","timestamp":1738061484000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/33\/1\/95\/7416509"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,17]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2,27]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzad026","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"type":"print","value":"1367-0751"},{"type":"electronic","value":"1368-9894"}],"subject":[],"published-other":{"date-parts":[[2025,2]]},"published":{"date-parts":[[2023,11,17]]}}}