{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:40:23Z","timestamp":1777516823299,"version":"3.51.4"},"reference-count":9,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,11,21]],"date-time":"2019-11-21T00:00:00Z","timestamp":1574294400000},"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>A computable structure [Formula: see text] has degree of categoricity d if d is exactly the degree of difficulty of computing isomorphisms between isomorphic computable copies of [Formula: see text]. Fokina, Kalimullin, and Miller showed that every degree d.c.e. in and above [Formula: see text], for any [Formula: see text], and also the degree [Formula: see text], are degrees of categoricity. Later, Csima, Franklin, and Shore showed that every degree [Formula: see text] for any computable ordinal \u03b1, and every degree d.c.e. in and above [Formula: see text] for any successor ordinal \u03b1, is a degree of categoricity. We show that every degree c.e. in and above [Formula: see text], for \u03b1 a limit ordinal, is a degree of categoricity. We also show that every degree c.e. in and above [Formula: see text] is the degree of categoricity of a prime model, making progress towards a question of Bazhenov and Marchuk.<\/jats:p>","DOI":"10.3233\/com-190254","type":"journal-article","created":{"date-parts":[[2019,11,24]],"date-time":"2019-11-24T12:40:44Z","timestamp":1574599244000},"page":"127-137","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Degrees of categoricity above limit ordinals"],"prefix":"10.1177","volume":"9","author":[{"given":"Barbara F.","family":"Csima","sequence":"first","affiliation":[{"name":"Pure Mathematics, University of Waterloo, Waterloo, ON, Canada."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Deveau","sequence":"additional","affiliation":[{"name":"Pure Mathematics, University or Waterloo, Waterloo, ON, Canada."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew","family":"Harrison-Trainor","sequence":"additional","affiliation":[{"name":"Department first, Victoria University of Wellington, Wellington, New Zealand."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Assem","family":"Mahmoud","sequence":"additional","affiliation":[{"name":"Pure Mathematics, University of Waterloo, Waterloo, ON, Canada."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,11,21]]},"reference":[{"key":"ref001","unstructured":"C.J.\u00a0Ash and J.\u00a0Knight, Computable Structures and the Hyperarithmetical Hierarchy, Elsevier, 2000."},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-94418-0_4"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2017.70"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-1960479"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2018.08.012"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-009-0160-4"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1134\/S0081543811060071"},{"key":"ref008","unstructured":"M.J.\u00a0Groszek and T.A.\u00a0Slaman, Moduli of computation, Talk presented at the\n                      Conference on Logic, Computability and Randomness\n                      , Buenos Aires, Argentina, 2007. https:\/\/math.berkeley.edu\/~slaman\/talks\/buenos_aries.pdf."},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1071505769"}],"container-title":["Computability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-190254","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/COM-190254","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-190254","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T16:00:12Z","timestamp":1777392012000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/COM-190254"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,21]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,5,13]]}},"alternative-id":["10.3233\/COM-190254"],"URL":"https:\/\/doi.org\/10.3233\/com-190254","relation":{},"ISSN":["2211-3568","2211-3576"],"issn-type":[{"value":"2211-3568","type":"print"},{"value":"2211-3576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,21]]}}}