{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T19:50:22Z","timestamp":1773258622824,"version":"3.50.1"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p> For countable structure, \"Scott rank\" provides a measure of internal, model-theoretic complexity. For a computable structure, the Scott rank is at most [Formula: see text]. There are familiar examples of computable structures of various computable ranks, and there is an old example of rank [Formula: see text]. In the present paper, we show that there is a computable structure of Scott rank [Formula: see text]. We give two different constructions. The first starts with an arithmetical example due to Makkai, and codes it into a computable structure. The second re-works Makkai's construction, incorporating an idea of Sacks. <\/jats:p>","DOI":"10.1142\/s0219061310000912","type":"journal-article","created":{"date-parts":[[2011,5,10]],"date-time":"2011-05-10T06:04:14Z","timestamp":1305007454000},"page":"31-43","source":"Crossref","is-referenced-by-count":8,"title":["COMPUTABLE STRUCTURES OF RANK $\\omega_{1}^{{\\rm CK}}$"],"prefix":"10.1142","volume":"10","author":[{"given":"J. F.","family":"KNIGHT","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Notre Dame, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"MILLAR","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Notre Dame, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90038-8"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90004-L"},{"key":"rf3","volume-title":"Computable Structures and the Hyperarithmetical Hierarchy","author":"Ash C. J.","year":"2000"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90015-8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.2307\/2274481"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1082418544"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.02.001"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1968-0244049-7"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.2307\/2273623"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80009-8"},{"key":"rf11","unstructured":"G. E.\u00a0Sacks, Higher Recursion Theory (Springer-Verlag, Berlin)\u00a0pp. 8\u201318."},{"key":"rf12","unstructured":"D.\u00a0Scott, The Theory of Models, eds. J.\u00a0Addison, L.\u00a0Henkin and A.\u00a0Tarski (North-Holland, 1965)\u00a0pp. 329\u2013341."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19960420139"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061310000912","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T14:16:42Z","timestamp":1565101002000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061310000912"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":13,"journal-issue":{"issue":"01n02","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2010,6]]}},"alternative-id":["10.1142\/S0219061310000912"],"URL":"https:\/\/doi.org\/10.1142\/s0219061310000912","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}