{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T01:25:07Z","timestamp":1660267507091},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":6437,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[1996,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We announce and explain recent results on the computably enumerable (c.e.) sets, especially their <jats:italic>definability<\/jats:italic> properties (as sets in the spirit of Cantor), their <jats:italic>automorphisms<\/jats:italic> (in the spirit of Felix Klein's <jats:italic>Erlanger Programm<\/jats:italic>), their <jats:italic>dynamic<\/jats:italic> properties, expressed in terms of how <jats:italic>quickly<\/jats:italic> elements enter them relative to elements entering other sets, and the <jats:italic>Martin Invariance Conjecture<\/jats:italic> on their Turing degrees, i.e., their <jats:italic>information content<\/jats:italic> with respect to relative computability (Turing reducibility).<\/jats:p>","DOI":"10.2307\/421110","type":"journal-article","created":{"date-parts":[[2006,5,7]],"date-time":"2006-05-07T03:08:56Z","timestamp":1146971336000},"page":"199-213","source":"Crossref","is-referenced-by-count":12,"title":["Definability, Automorphisms, and Dynamic Properties of Computably Enumerable Sets"],"prefix":"10.1017","volume":"2","author":[{"given":"Leo","family":"Harrington","sequence":"first","affiliation":[]},{"given":"Robert I.","family":"Soare","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600008751_ref004","unstructured":"[4] Harrington L. and Soare R. I. , Codable sets and orbits of computably enumerable sets, Journal of Symbolic Logic , to appear."},{"key":"S1079898600008751_ref013","doi-asserted-by":"crossref","unstructured":"[13] Soare R. I. , Computability and recursion, to appear, 1996.","DOI":"10.2307\/420992"},{"key":"S1079898600008751_ref006","unstructured":"[6] Harrington L. , Martins invariance conjecture and low sets, in preparation."},{"key":"S1079898600008751_ref007","unstructured":"[7] Harrington L. , The -automorphism method and noninvariant classes of degrees, Journal of the American Mathematical Society , to appear."},{"key":"S1079898600008751_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1097164-6"},{"key":"S1079898600008751_ref008","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.88.22.10242"},{"key":"S1079898600008751_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0541"},{"key":"S1079898600008751_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S1079898600008751_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(92)90065-S"},{"key":"S1079898600008751_ref011","volume-title":"Handbook of computability theory","author":"Soare"},{"key":"S1079898600008751_ref009","volume-title":"Computability, enumerability, unsolvability: Directions in recursion theory","author":"Harrington","year":"1994"},{"key":"S1079898600008751_ref010","unstructured":"[10] Soare R. I. , Computability and enumerability, Proceedings of the 10th International Congress for Logic, Methodology and the Philosophy of Science, Section 3: Recursion Theory and Constructivism, Florence, August 19\u201325, 1995 , to appear."},{"key":"S1079898600008751_ref005","unstructured":"[5] Harrington L. , Definable properties of the computably enumerable sets, in preparation."}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600008751","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T17:24:32Z","timestamp":1557681872000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600008751\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,6]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,6]]}},"alternative-id":["S1079898600008751"],"URL":"https:\/\/doi.org\/10.2307\/421110","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,6]]}}}