{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T13:22:20Z","timestamp":1648819340671},"reference-count":13,"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>This paper concerns automorphisms of the computably enumerable sets. We prove two results relating semilow sets and prompt degrees via automorphisms, one of which is complementary to a recent result of Downey and Harrington. We also show that the property of effective simplicity is not invariant under automorphism, and that in fact every promptly simple set is automorphic to an effectively simple set. A major technique used in these proofs is a modification of the Harrington-Soare version of the method of Harrington-Soare and Cholak for constructing \u0394<jats:sub arrange=\"stack\">3<\/jats:sub><jats:sup arrange=\"stack\">0<\/jats:sup> automorphisms; this modification takes advantage of a recent result of Soare on the extension of \u201crestricted\u201d automorphisms to full automorphisms.<\/jats:p>","DOI":"10.2178\/jsl\/1190150103","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:13:31Z","timestamp":1197555211000},"page":"649-678","source":"Crossref","is-referenced-by-count":1,"title":["On orbits, of prompt and low computably enumerable sets"],"prefix":"10.1017","volume":"67","author":[{"given":"Kevin","family":"Wald","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009671_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1944-08111-1"},{"key":"S0022481200009671_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/1970842"},{"key":"S0022481200009671_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(97)00065-1"},{"key":"S0022481200009671_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0541"},{"key":"S0022481200009671_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200009671_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(92)90065-S"},{"key":"S0022481200009671_ref004","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.88.22.10242"},{"key":"S0022481200009671_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-96-00181-6"},{"key":"S0022481200009671_ref006","first-page":"809","volume":"47","author":"Maass","year":"1982","journal-title":"Recursively enumerable generic sets"},{"key":"S0022481200009671_ref008","unstructured":"Robinson R. W. , The inclusion lattice and degrees of unsolvability of the recursively enumerable sets, Ph. d. dissertation , Cornell University, 1966."},{"key":"S0022481200009671_ref009","unstructured":"Soare R. I. , Templates, extensions, and automorphisms, to appear."},{"key":"S0022481200009671_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(82)90016-X"},{"key":"S0022481200009671_ref013","unstructured":"Wald K. M. , Automorphisms and noninvariant properties of the computably enumerable sets, Ph. d. dissertation , University of Chicago, 1999."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009671","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T21:06:29Z","timestamp":1557176789000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009671\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S0022481200009671"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150103","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}