{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T05:15:18Z","timestamp":1735881318252,"version":"3.32.0"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T00:00:00Z","timestamp":1687478400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper proves the finite axiomatizability of transitive modal logics of finite depth and finite width w.r.t. proper-successor-equivalence. The frame condition of the latter requires, in a rooted transitive frame, a finite upper bound of cardinality for antichains of points with different sets of proper successors. The result generalizes Rybakov\u2019s result of the finite axiomatizability of extensions of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000175_inline1.png\"\/><jats:tex-math>\n$\\mathbf {S4}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> of finite depth and finite width.<\/jats:p>","DOI":"10.1017\/s1755020323000175","type":"journal-article","created":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T18:34:38Z","timestamp":1687545278000},"page":"951-964","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["FINITE AXIOMATIZABILITY OF TRANSITIVE MODAL LOGICS OF FINITE DEPTH AND WIDTH WITH RESPECT TO PROPER-SUCCESSOR-EQUIVALENCE"],"prefix":"10.1017","volume":"17","author":[{"given":"YAN","family":"ZHANG","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MING","family":"XU","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,6,23]]},"reference":[{"key":"S1755020323000175_r11","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-021-09943-4"},{"key":"S1755020323000175_r12","first-page":"16","article-title":"Finite axiomatizability of transitive logics of finite depth and finite weak width","volume":"12","author":"Zhang","year":"2019","journal-title":"Studies in Logic"},{"key":"S1755020323000175_r2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537793.001.0001","volume-title":"Modal Logic","volume":"35","author":"Chagrov","year":"1997"},{"volume-title":"An Essay in Classical Modal Logic","year":"1971","author":"Segerberg","key":"S1755020323000175_r9"},{"key":"S1755020323000175_r5","doi-asserted-by":"publisher","DOI":"10.2307\/2272340"},{"key":"S1755020323000175_r6","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90022-E"},{"key":"S1755020323000175_r3","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19710170141"},{"key":"S1755020323000175_r4","doi-asserted-by":"publisher","DOI":"10.1111\/j.1755-2567.1974.tb00081.x"},{"key":"S1755020323000175_r7","doi-asserted-by":"publisher","DOI":"10.2307\/2273624"},{"key":"S1755020323000175_r8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01877236"},{"key":"S1755020323000175_r1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"S1755020323000175_r10","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-012-9398-7"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020323000175","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,2]],"date-time":"2025-01-02T10:53:28Z","timestamp":1735815208000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020323000175\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,23]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["S1755020323000175"],"URL":"https:\/\/doi.org\/10.1017\/s1755020323000175","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"type":"print","value":"1755-0203"},{"type":"electronic","value":"1755-0211"}],"subject":[],"published":{"date-parts":[[2023,6,23]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}