{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:09:17Z","timestamp":1772514557722,"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":3845,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2003,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that if <jats:italic>A<\/jats:italic> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200008665_inline1\"\/> are automorphic via \u03a6 then the structures <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200008665_inline2\"\/>(<jats:italic>A<\/jats:italic>) and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200008665_inline2\"\/>(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200008665_inline1\"\/>) are \u0394<jats:sub arrange=\"stack\">3<\/jats:sub><jats:sup arrange=\"stack\">0<\/jats:sup>-isomorphic via an isomorphism \u03a8 induced by \u03a6. Then we use this result to classify completely the orbits of hhsimple sets.<\/jats:p>","DOI":"10.2178\/jsl\/1058448453","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:12:32Z","timestamp":1109797952000},"page":"1044-1064","source":"Crossref","is-referenced-by-count":5,"title":["Isomorphisms of splits of computably enumerable sets"],"prefix":"10.1017","volume":"68","author":[{"given":"Peter A.","family":"Cholak","sequence":"first","affiliation":[]},{"given":"Leo A.","family":"Harrington","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200008665_ref010","first-page":"397","volume":"50","author":"Montagna","year":"1985","journal-title":"Universal recursion-theoretic properties of r. e. preordered structures"},{"key":"S0022481200008665_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-96-00181-6"},{"key":"S0022481200008665_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90234-5"},{"key":"S0022481200008665_ref007","doi-asserted-by":"publisher","DOI":"10.1006\/aima.1997.1687"},{"key":"S0022481200008665_ref011","doi-asserted-by":"publisher","DOI":"10.1112\/S0024609397003548"},{"key":"S0022481200008665_ref005","first-page":"175","volume-title":"Annals of Pure and Applied Logic","volume":"59","author":"Downey","year":"1993"},{"key":"S0022481200008665_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0541"},{"key":"S0022481200008665_ref002","volume-title":"Extension theorems, orbits and automorphisms of the computably enumerable sets","author":"Cholak","year":"2002"},{"key":"S0022481200008665_ref012","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-00-02652-0"},{"key":"S0022481200008665_ref014","unstructured":"Stob M. , The structure and elementary theory of the recursive enumerable sets, Ph.D. thesis , University of Chicago, 1979."},{"key":"S0022481200008665_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200008665_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/421206"},{"key":"S0022481200008665_ref009","first-page":"51","volume":"49","author":"Maass","year":"1984","journal-title":"On the orbit of hyperhypersimple sets"},{"key":"S0022481200008665_ref003","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061302000151"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200008665","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T22:42:39Z","timestamp":1557182559000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200008665\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,9]]}},"alternative-id":["S0022481200008665"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1058448453","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,9]]}}}