{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T17:16:33Z","timestamp":1671815793734},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1745,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,6]]},"abstract":"Abstract<\/jats:title>We examine the effective categoricity of equivalence structures via Ershov's difference hierarchy. We explore various kinds of categoricity available by distinguishing three different notions of isomorphism available in this hierarchy. We prove several results relating our notions of categoricity to computable equivalence relations: for example, we show that, for such relations, computable categoricity is equivalent to our notion of weak \u03c9<\/jats:italic>-c.e. categoricity, and that -categoricity is equivalent to our notion of graph-\u03c9<\/jats:italic>-c.e. categoricity.<\/jats:p>","DOI":"10.2178\/jsl\/1243948326","type":"journal-article","created":{"date-parts":[[2009,6,2]],"date-time":"2009-06-02T13:12:25Z","timestamp":1243948345000},"page":"535-556","source":"Crossref","is-referenced-by-count":9,"title":["Equivalence structures and isomorphisms in the difference hierarchy"],"prefix":"10.1017","volume":"74","author":[{"given":"Douglas","family":"Cenzer","sequence":"first","affiliation":[]},{"given":"Geoffrey","family":"Laforte","sequence":"additional","affiliation":[]},{"given":"Jeffrey","family":"Remmel","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003558_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200003558_ref002","first-page":"68","article-title":"Constructive abelian p-groups","volume":"2","author":"Khisamiev","year":"1992","journal-title":"Siberian Advances in Mathematics"},{"key":"S0022481200003558_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.10.002"},{"key":"S0022481200003558_ref003","unstructured":"Khoussainov B. , Stephan F. , and Yang Y. , Computable categoricity and the Ershov hierarchy, unpublished."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003558","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T13:26:13Z","timestamp":1556630773000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003558\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,6]]}},"alternative-id":["S0022481200003558"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1243948326","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}