{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T05:20:47Z","timestamp":1774588847545,"version":"3.50.1"},"reference-count":8,"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":4302,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is proved that if 1 &lt; <jats:italic>m<\/jats:italic> &lt; 2<jats:sub><jats:italic>p<\/jats:italic><\/jats:sub> \u2264 <jats:italic>n<\/jats:italic> for some integer <jats:italic>p<\/jats:italic> then the elementary theories of posets of <jats:italic>m<\/jats:italic>-c.e. and <jats:italic>n<\/jats:italic>-c.e. e-degrees are distinct. It is proved also that the structures \u3008<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009609_inline1\"\/><jats:sub>2<jats:italic>n<\/jats:italic><\/jats:sub>, \u2264, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009609_inline1\"\/>\u3009 and \u3008<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009609_inline1\"\/><jats:sub>2<jats:italic>n<\/jats:italic><\/jats:sub>, \u2264. <jats:italic>P<\/jats:italic>\u3009 are not elementary equivalent where <jats:italic>P<\/jats:italic> is the predicate <jats:italic>P<\/jats:italic>(<jats:italic><jats:bold>a<\/jats:bold><\/jats:italic>) = \u201c<jats:italic><jats:bold>a<\/jats:bold><\/jats:italic> is a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009609_inline2\"\/> e-degree\u201d.<\/jats:p>","DOI":"10.2178\/jsl\/1190150096","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:13:31Z","timestamp":1197573211000},"page":"537-546","source":"Crossref","is-referenced-by-count":3,"title":["Splitting properties of <i>n<\/i>-c.e. enumeration degrees"],"prefix":"10.1017","volume":"67","author":[{"given":"I. SH.","family":"Kalimullin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009609_ref006","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200009609_ref003","first-page":"57","volume-title":"Recursion theory week, Oberwolfach 1989","volume":"1432","author":"Cooper","year":"1990"},{"key":"S0022481200009609_ref007","volume-title":"Izvestija VUZov, Matematika","author":"Kalimullin"},{"key":"S0022481200009609_ref004","first-page":"57","volume-title":"Recursion theory week, Oberwolfach 1989","volume":"1432","author":"Cooper","year":"1990"},{"key":"S0022481200009609_ref001","first-page":"195","volume":"50","author":"Ahmad","year":"1991","journal-title":"Embedding the diamond in the \u03a32 enumeration degrees"},{"key":"S0022481200009609_ref002","volume-title":"Archive for Mathematical Logic","author":"Arslanov"},{"key":"S0022481200009609_ref005","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/21.1.43"},{"key":"S0022481200009609_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009609","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T01:06:00Z","timestamp":1557191160000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009609\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S0022481200009609"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150096","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}