{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:09:31Z","timestamp":1753884571098,"version":"3.41.2"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"the European Union\u2019s Horizon 2020 Research and Innovation Programme under the Marie Sk\u0142odowska-Curie","award":["101026834 \u2014 ACOSE"],"award-info":[{"award-number":["101026834 \u2014 ACOSE"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:p> In this paper, we give a characterization of the strong degrees of categoricity of computable structures greater or equal to [Formula: see text]. They are precisely the treeable degrees\u00a0\u2014 the least degrees of paths through computable trees \u2014 that compute [Formula: see text]. As a corollary, we obtain several new examples of degrees of categoricity. Among them we show that every degree [Formula: see text] with [Formula: see text] for [Formula: see text] a computable ordinal greater than 2 is the strong degree of categoricity of a rigid structure. Using quite different techniques we show that every degree [Formula: see text] with [Formula: see text] is the strong degree of categoricity of a structure. Together with the above example this answers a question of Csima and Ng. To complete the picture we show that there is a degree [Formula: see text] with [Formula: see text] that is not the degree of categoricity of a rigid structure. <\/jats:p>","DOI":"10.1142\/s0219061324500028","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T13:57:23Z","timestamp":1689083843000},"source":"Crossref","is-referenced-by-count":0,"title":["Degrees of categoricity and treeable degrees"],"prefix":"10.1142","volume":"24","author":[{"given":"Barbara F.","family":"Csima","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dino","family":"Rossegger","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California, Berkeley, USA"},{"name":"Institute of Discrete Mathematics and Geometry, Technische Universit\u00e4t Wien, Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,8,11]]},"reference":[{"key":"S0219061324500028BIB001","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-3496154"},{"key":"S0219061324500028BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2017.70"},{"key":"S0219061324500028BIB003","doi-asserted-by":"publisher","DOI":"10.1134\/S1995080220090048"},{"key":"S0219061324500028BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-58741-7_16"},{"key":"S0219061324500028BIB005","doi-asserted-by":"publisher","DOI":"10.3233\/COM-190254"},{"key":"S0219061324500028BIB006","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-1960479"},{"key":"S0219061324500028BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061322500222"},{"key":"S0219061324500028BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2018.08.012"},{"key":"S0219061324500028BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-009-0160-4"},{"key":"S0219061324500028BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-50062-1_20"},{"key":"S0219061324500028BIB011","doi-asserted-by":"publisher","DOI":"10.3233\/COM-140027"},{"issue":"950","key":"S0219061324500028BIB012","first-page":"407","volume":"248","author":"Fr\u00f6hlich A.","year":"1956","journal-title":"Philos. 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