{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:37:03Z","timestamp":1753889823574,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T00:00:00Z","timestamp":1532563200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T00:00:00Z","timestamp":1532563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T00:00:00Z","timestamp":1532563200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>In the final chain of the countable powerset functor, we show that the set at index $\\omega_1$, regarded as a transition system, is not strongly extensional because it contains a &amp;quot;ghost&amp;quot; element that has no successor even though its component at each successor index is inhabited. The method, adapted from a construction of Forti and Honsell, also gives ghosts at larger ordinals in the final chain of other subfunctors of the powerset functor. This leads to a precise description of which sets in these final chains are strongly extensional.<\/jats:p>","DOI":"10.23638\/lmcs-14(3:4)2018","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:29:15Z","timestamp":1743701355000},"source":"Crossref","is-referenced-by-count":0,"title":["A Ghost at $\\omega_1$"],"prefix":"10.23638","volume":"Volume 14, Issue 3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0864-1876","authenticated-orcid":false,"given":"Paul Blain","family":"Levy","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2018,7,26]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1612.09514v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1612.09514v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:29:15Z","timestamp":1743701355000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2626"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,26]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-14(3:4)2018","relation":{"has-preprint":[{"id-type":"arxiv","id":"1612.09514v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.09514v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.09514v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.09514v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1612.09514","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1612.09514","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2018,7,26]]},"article-number":"2626"}}