{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:17Z","timestamp":1753894397475,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Boolean locales are \"almost discrete\", in the sense that a spatial Boolean\nlocale is just a discrete locale (that is, it corresponds to the frame of open\nsubsets of a discrete space, namely the powerset of a set). This basic fact,\nhowever, cannot be proven constructively, that is, over intuitionistic logic,\nas it requires the full law of excluded middle (LEM). In fact, discrete locales\nare never Boolean constructively, except for the trivial locale. So, what is an\nalmost discrete locale constructively? Our claim is that Sambin's overlap\nalgebras have good enough features to deserve to be called that. Namely, they\ninclude the class of discrete locales, they arise as smallest strongly dense\nsublocales (of overt locales), and hence they coincide with the Boolean locales\nif LEM holds.<\/jats:p>","DOI":"10.46298\/lmcs-19(4:21)2023","type":"journal-article","created":{"date-parts":[[2023,12,10]],"date-time":"2023-12-10T22:10:08Z","timestamp":1702246208000},"source":"Crossref","is-referenced-by-count":0,"title":["Overlap Algebras as Almost Discrete Locales"],"prefix":"10.46298","volume":"Volume 19, Issue 4","author":[{"given":"Francesco","family":"Ciraulo","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2023,12,8]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/12671\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/12671\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,10]],"date-time":"2023-12-10T22:10:09Z","timestamp":1702246209000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/7525"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,8]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-19(4:21)2023","relation":{"has-preprint":[{"id-type":"arxiv","id":"1601.04830v5","asserted-by":"subject"},{"id-type":"arxiv","id":"1601.04830v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1601.04830v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1601.04830v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1601.04830","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1601.04830","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2023,12,8]]},"article-number":"7525"}}