{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:21:21Z","timestamp":1775053281409,"version":"3.50.1"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1653,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,9]]},"abstract":"Abstract<\/jats:title>We show that for every computable limit ordinal \u03b1<\/jats:italic>, there is a computable structure that is categorical, but not relatively categorical (equivalently, it does not have a formally Scott family). We also show that for every computable limit ordinal \u03b1<\/jats:italic>, there is a computable structure with an additional relation R<\/jats:italic> that is intrinsically on , but not relatively intrinsically on (equivalently, it is not definable by a computable \u03a3\u03b1<\/jats:italic><\/jats:sub> formula with finitely many parameters). Earlier results in [7], [10], and [8] establish the same facts for computable successor ordinals \u03b1<\/jats:italic>.<\/jats:p>","DOI":"10.2178\/jsl\/1245158098","type":"journal-article","created":{"date-parts":[[2009,6,16]],"date-time":"2009-06-16T13:16:09Z","timestamp":1245158169000},"page":"1047-1060","source":"Crossref","is-referenced-by-count":19,"title":["Intrinsic bounds on complexity and definability at limit levels"],"prefix":"10.1017","volume":"74","author":[{"given":"John","family":"Chisholm","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ekaterina B.","family":"Fokina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergey S.","family":"Goncharov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valentina S.","family":"Harizanov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julia F.","family":"Knight","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sara","family":"Quinn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003431_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BF01877237"},{"key":"S0022481200003431_ref011","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200003431_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01668593"},{"key":"S0022481200003431_ref013","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19960420139"},{"key":"S0022481200003431_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90015-8"},{"key":"S0022481200003431_ref003","volume-title":"Computable structures and the hyperarithmetical hierarchy","author":"Ash","year":"2000"},{"key":"S0022481200003431_ref007","first-page":"257","article-title":"The number of nonautoequivalent constructivizations","volume":"16","author":"Gon\u010darov","year":"1977","journal-title":"Algebra and Logic"},{"key":"S0022481200003431_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1990-0955487-0"},{"key":"S0022481200003431_ref014","first-page":"563","volume":"49","author":"Watnick","year":"1984","journal-title":"A generalization of Tennenbaum's theorem on effectively finite recursive linear orderings"},{"key":"S0022481200003431_ref006","first-page":"1168","volume":"55","author":"Chisholm","year":"1990","journal-title":"Effective model theory vs. recursive model theory"},{"key":"S0022481200003431_ref001","first-page":"673","volume":"56","author":"Ash","year":"1991","journal-title":"A construction for recursive linear orderings"},{"key":"S0022481200003431_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.02.001"},{"key":"S0022481200003431_ref009","first-page":"585","volume":"69","author":"Goncharov","year":"2004","journal-title":"relations and paths through"},{"key":"S0022481200003431_ref010","volume-title":"Techniques and counterexamples in almost categorical recursive model theory","author":"Manasse","year":"1982"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003431","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T11:24:06Z","timestamp":1556623446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003431\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["S0022481200003431"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1245158098","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}