{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T22:04:26Z","timestamp":1747173866406,"version":"3.40.5"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T00:00:00Z","timestamp":1648425600000},"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":[[2024,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In topological modal logic, it is well known that the Cantor derivative is more expressive than the topological closure, and the \u2018elsewhere\u2019, or \u2018difference\u2019, operator is more expressive than the \u2018somewhere\u2019 operator. In 2014, Kudinov and Shehtman asked whether the combination of closure and elsewhere becomes strictly more expressive when adding the Cantor derivative. In this paper we give an affirmative answer: in fact, the Cantor derivative alone can define properties of topological spaces not expressible with closure and elsewhere. To prove this, we develop a novel theory of morphisms which preserve formulas with the elsewhere operator.<\/jats:p>","DOI":"10.1017\/s1755020322000120","type":"journal-article","created":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T10:55:38Z","timestamp":1648464938000},"page":"144-153","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["TAMING THE \u2018ELSEWHERE\u2019: ON EXPRESSIVITY OF TOPOLOGICAL LANGUAGES"],"prefix":"10.1017","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8604-4183","authenticated-orcid":false,"given":"DAVID","family":"FERN\u00c1NDEZ-DUQUE","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,3,28]]},"reference":[{"key":"S1755020322000120_r16","first-page":"244","volume-title":"ECAI 2000","author":"Wolter","year":"2000"},{"key":"S1755020322000120_r3","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-005-4648-6"},{"key":"S1755020322000120_r15","doi-asserted-by":"publisher","DOI":"10.1080\/11663081.1999.10510972"},{"key":"S1755020322000120_r9","first-page":"319","volume-title":"Advances in Modal Logic 6","author":"Kudinov","year":"2006"},{"key":"S1755020322000120_r5","doi-asserted-by":"publisher","DOI":"10.2307\/2274663"},{"key":"S1755020322000120_r12","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-011-9305-7"},{"key":"S1755020322000120_r7","unstructured":"[7] Gabelaia, D. (2001). Modal Definability in Topology. 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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"}}]}}