{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T15:49:30Z","timestamp":1762444170271},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,1,22]],"date-time":"2010-01-22T00:00:00Z","timestamp":1264118400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. symb. logic"],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:p>We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is<jats:bold>K4<\/jats:bold>and the modal logic of weakly scattered Stone spaces is<jats:bold>K4G<\/jats:bold>. As a corollary, we obtain that<jats:bold>K4<\/jats:bold>is also the modal logic of compact Hausdorff spaces and<jats:bold>K4G<\/jats:bold>is the modal logic of weakly scattered compact Hausdorff spaces.<\/jats:p>","DOI":"10.1017\/s1755020309990335","type":"journal-article","created":{"date-parts":[[2010,1,22]],"date-time":"2010-01-22T11:50:42Z","timestamp":1264161042000},"page":"26-40","source":"Crossref","is-referenced-by-count":11,"title":["THE MODAL LOGIC OF STONE SPACES: DIAMOND AS DERIVATIVE"],"prefix":"10.1017","volume":"3","author":[{"given":"GURAM","family":"BEZHANISHVILI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LEO","family":"ESAKIA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DAVID","family":"GABELAIA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,1,22]]},"reference":[{"key":"S1755020309990335_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(96)00114-9"},{"key":"S1755020309990335_ref12","unstructured":"Shehtman V. (1990). Derived sets in Euclidean spaces and modal logic. Preprint X-90-05, University of Amsterdam."},{"key":"S1755020309990335_ref11","doi-asserted-by":"publisher","DOI":"10.2307\/1969080"},{"key":"S1755020309990335_ref10","unstructured":"Gabelaia D. (2004). Topological semantics and two-dimensional combinations of modal logics. PhD Thesis, King\u2019s College, London."},{"key":"S1755020309990335_ref8","first-page":"292","volume-title":"Logical Investigations, No. 9","author":"Esakia","year":"2002"},{"key":"S1755020309990335_ref7","first-page":"128","volume-title":"Studies in logic and semantics","author":"Esakia","year":"1981"},{"key":"S1755020309990335_ref6","volume-title":"General Topology","author":"Engelking","year":"1977"},{"key":"S1755020309990335_ref5","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537793.001.0001","volume-title":"Modal Logic","author":"Chagrov","year":"1997"},{"key":"S1755020309990335_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-010-0175-x"},{"key":"S1755020309990335_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-005-4648-6"},{"key":"S1755020309990335_ref1","first-page":"49","volume-title":"Intensional logics and the logical structure of theories","author":"Abashidze","year":"1988"},{"key":"S1755020309990335_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2003.11.013"},{"key":"S1755020309990335_ref2","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/13.6.889"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020309990335","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,23]],"date-time":"2024-03-23T02:39:14Z","timestamp":1711161554000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020309990335\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,22]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["S1755020309990335"],"URL":"https:\/\/doi.org\/10.1017\/s1755020309990335","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1,22]]}}}