{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:40:17Z","timestamp":1777516817688,"version":"3.51.4"},"reference-count":10,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2020,5,8]],"date-time":"2020-05-08T00:00:00Z","timestamp":1588896000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Computability"],"published-print":{"date-parts":[[2020,5,13]]},"abstract":"<jats:p>The range of possible ordinal values for the Cantor\u2013Bendixson rank of an effectively closed set in Cantor space, and the relationship between the ranks and the Turing degrees of its members, have been closely studied. The wide array of results on this topic have often made use of useful topological features of Cantor space (notably, compactness) and of key properties of computable well-orders. In this paper, a number of these results are extended to the case of Cantor space on the first uncountable ordinal, in which these properties do not hold, using admissible recursion theory.<\/jats:p>","DOI":"10.3233\/com-180187","type":"journal-article","created":{"date-parts":[[2020,5,8]],"date-time":"2020-05-08T14:46:22Z","timestamp":1588949182000},"page":"111-125","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Cantor\u2013Bendixson ranks of effectively closed sets in admissible recursion theory"],"prefix":"10.1177","volume":"9","author":[{"given":"Reese","family":"Johnston","sequence":"first","affiliation":[{"name":"Robinson Center for Young Scholars, University of Washington, Seattle, WA, United States."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,5,8]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(86)90067-9"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0099164"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139028592.005"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2019.5"},{"key":"ref005","unstructured":"A.S.\u00a0Kechris, Classical Descriptive Set Theory, Springer, Berlin, 2012."},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.2307\/2267778"},{"key":"ref007","first-page":"161","volume":"29","author":"Kripke S.","year":"1964","journal-title":"Journal of Symbolic Logic"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12013-2"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1976-0424544-2"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71118-2"}],"container-title":["Computability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-180187","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/COM-180187","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-180187","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T16:00:11Z","timestamp":1777392011000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/COM-180187"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,8]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,5,13]]}},"alternative-id":["10.3233\/COM-180187"],"URL":"https:\/\/doi.org\/10.3233\/com-180187","relation":{},"ISSN":["2211-3568","2211-3576"],"issn-type":[{"value":"2211-3568","type":"print"},{"value":"2211-3576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,8]]}}}