{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T12:08:48Z","timestamp":1765368528087},"reference-count":5,"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":8320,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:p>Since its introduction in [K1-Po], the upper semilattice of Turing degrees has been an object of fascination to practitioners of the recursion-theoretic art. Starting from relatively simple concepts and definitions, it has turned out to be a structure of enormous complexity and richness. This paper is a contribution to the ongoing study of this structure.<\/jats:p><jats:p>Much of the work on Turing degrees may be formulated in terms of the embeddability of certain first-order structures in a structure whose universe is some set of degrees and whose relations, functions, and constants are natural degree-theoretic ones. Thus, for example, we know that if {<jats:italic>P<\/jats:italic>, \u2264<jats:sub><jats:italic>P<\/jats:italic><\/jats:sub>) is a partial ordering of cardinality at most \u2135<jats:sub>1<\/jats:sub> which is locally countable\u2014each point has at most countably many predecessors\u2014then there is an embedding<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200024555_eqnU1\" \/><\/jats:disp-formula><\/jats:p><jats:p>where <jats:bold>D<\/jats:bold> is the set of all Turing degrees and &lt;<jats:sub>T<\/jats:sub> is Turing reducibility. If (<jats:italic>P<\/jats:italic>, \u2264<jats:sub><jats:italic>P<\/jats:italic><\/jats:sub>) is a countable partial ordering, then the image of the embedding may be taken to be a subset of <jats:bold>R<\/jats:bold>, the set of recursively enumerable degrees. Without attempting to make the notion completely precise, we shall call embeddings of the first sort <jats:italic>global<\/jats:italic>, in contrast to <jats:italic>local<\/jats:italic> embeddings which impose some restrictions on the image set.<\/jats:p>","DOI":"10.2307\/2274700","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:39:41Z","timestamp":1146955181000},"page":"563-591","source":"Crossref","is-referenced-by-count":5,"title":["Jump embeddings in the Turing degrees"],"prefix":"10.1017","volume":"56","author":[{"given":"Peter G.","family":"Hinman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Theodore A.","family":"Slaman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200024555_ref004","unstructured":"Simpson M. F. , \u03c9-REA operators and the range of the \u03c9-jump on degrees below 0\u03c9 , manuscript derived from Ph.D. dissertation, Cornell University, Ithaca, New York, 1985."},{"key":"S0022481200024555_ref003","unstructured":"Shore R. A. , Private communication."},{"key":"S0022481200024555_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/1969708"},{"key":"S0022481200024555_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200024555_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1968-0244049-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200024555","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T21:45:16Z","timestamp":1558129516000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200024555\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["S0022481200024555"],"URL":"https:\/\/doi.org\/10.2307\/2274700","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}