{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T16:34:26Z","timestamp":1649003666449},"reference-count":31,"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":1380,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that there is a first order sentence \u03c6(<jats:italic>x: a, b, l<\/jats:italic>) such that for every computable partial order <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002668_inline1\" \/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002668_inline3\" \/>-degree <jats:italic><jats:bold>u<\/jats:bold><\/jats:italic> &gt; <jats:bold>0<\/jats:bold><jats:sub><jats:italic>e<\/jats:italic><\/jats:sub>, there are <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002668_inline3\" \/>-enumeration degrees <jats:italic><jats:bold>a<\/jats:bold><\/jats:italic> \u2264 <jats:italic><jats:bold>u<\/jats:bold><\/jats:italic>, <jats:italic><jats:bold>b<\/jats:bold><\/jats:italic>, and <jats:italic>l<\/jats:italic> such that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002668_inline02\" \/>. Allowing <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002668_inline1\" \/> to be a suitably defined standard model of arithmetic gives a parameterized interpretation of true arithmetic in the <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002668_inline3\" \/>-enumeration degrees. Finally we show that there is a first order sentence that correctly identifies a subset of the standard models, which gives a parameterless interpretation of true arithmetic in the <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002668_inline3\" \/>-enumeration degrees.<\/jats:p>","DOI":"10.2178\/jsl\/1268917493","type":"journal-article","created":{"date-parts":[[2010,3,18]],"date-time":"2010-03-18T09:05:57Z","timestamp":1268903157000},"page":"522-550","source":"Crossref","is-referenced-by-count":0,"title":["Interpreting true arithmetic in the -enumeration degrees"],"prefix":"10.1017","volume":"75","author":[{"given":"Thomas F.","family":"Kent","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002668_ref004","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19980440402"},{"key":"S0022481200002668_ref002","unstructured":"Ahmad S. , Some results on enumeration reducibility, Ph.D. thesis, Simon Frasier University, 1989."},{"key":"S0022481200002668_ref015","first-page":"69","volume":"67","author":"Lempp","year":"2002","journal-title":"Embedding finite lattices into the \u03a320 enumeration degrees"},{"key":"S0022481200002668_ref016","first-page":"839","article-title":"Jumps of quasi-minimal enumeration degrees","volume":"50","author":"Mcevoy","year":"1985","journal-title":"this Journal"},{"key":"S0022481200002668_ref001","volume-title":"Tbilisi Mathematical Journal","author":"Affitato"},{"key":"S0022481200002668_ref003","first-page":"195","volume":"56","author":"Ahmad","year":"1991","journal-title":"Embedding the diamond in the \u03a320 enumeration degrees"},{"key":"S0022481200002668_ref031","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/257\/04043"},{"key":"S0022481200002668_ref027","doi-asserted-by":"publisher","DOI":"10.2307\/1971028"},{"key":"S0022481200002668_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/s001530100078"},{"key":"S0022481200002668_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90003-9"},{"key":"S0022481200002668_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/BF01794984"},{"key":"S0022481200002668_ref018","first-page":"501","article-title":"Degrees of difficulty of the mass problem","volume":"104","author":"Medvedev","year":"1955","journal-title":"Doklady Akademii Nauk SSSR (N.S.)"},{"key":"S0022481200002668_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0086114"},{"key":"S0022481200002668_ref028","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050064"},{"key":"S0022481200002668_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190967"},{"key":"S0022481200002668_ref022","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(00)00021-X"},{"key":"S0022481200002668_ref010","doi-asserted-by":"publisher","DOI":"10.1006\/aima.1997.1687"},{"key":"S0022481200002668_ref011","first-page":"1284","volume":"71","author":"Kent","year":"2006","journal-title":"The \u03a03-theory of the \u03a320-enumeration degrees is undecidable"},{"key":"S0022481200002668_ref012","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-16.1.537"},{"key":"S0022481200002668_ref014","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061305000432"},{"key":"S0022481200002668_ref017","first-page":"839","volume":"50","author":"McEvoy","year":"1985","journal-title":"On minimal pairs of enumeration-degrees"},{"key":"S0022481200002668_ref019","unstructured":"Nies A. , Definability and undecidability in recursion theoretic semilattices, Ph.D. thesis, Ruprecht-Kals-Universit\u00e4t Heidelberg, 1994."},{"key":"S0022481200002668_ref020","first-page":"597","article-title":"The last question on recursively enumerable m-degrees","volume":"33","author":"Nies","year":"1994","journal-title":"Sibirski\u012d Fond Algebry i Logiki. 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