{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T07:35:36Z","timestamp":1772523336091,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2002,11]]},"abstract":"<jats:p> We show that the double jump is definable in the computably enumerable sets. Our main result is as follows: let [Formula: see text] is the Turing degree of a [Formula: see text] set J \u2265<jats:sub>T<\/jats:sub>0\u2033}. Let [Formula: see text] such that [Formula: see text] is upward closed in [Formula: see text]. Then there is an \u2112(A) property [Formula: see text] such that [Formula: see text] if and only if there is an A where A \u2261<jats:sub>T<\/jats:sub> F and [Formula: see text]. A corollary of this is that, for all n \u2265 2, the high <jats:sub>n<\/jats:sub> ([Formula: see text]) computably enumerable degrees are invariant in the computably enumerable sets. Our work resolves Martin's Invariance Conjecture. <\/jats:p>","DOI":"10.1142\/s0219061302000151","type":"journal-article","created":{"date-parts":[[2002,11,19]],"date-time":"2002-11-19T10:30:53Z","timestamp":1037701853000},"page":"261-296","source":"Crossref","is-referenced-by-count":13,"title":["ON THE DEFINABILITY OF THE DOUBLE JUMP IN THE COMPUTABLY ENUMERABLE SETS"],"prefix":"10.1142","volume":"02","author":[{"given":"PETER A.","family":"CHOLAK","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Notre Dame,   Notre Dame, IN 46556-5641, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LEO A.","family":"HARRINGTON","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California,  Berkeley, CA 94720-3840, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"issue":"541","key":"p_2","first-page":"0065","volume":"113","author":"Cholak P.","year":"1995","journal-title":"Mem. Amer. Math. Soc."},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1006\/aima.1997.1687"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.2307\/421110"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-96-00181-6"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.2307\/2270328"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1980.87.135"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760850"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19660120125"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.2307\/2271654"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.2307\/2272046"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061302000151","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:32:07Z","timestamp":1565094727000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061302000151"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,11]]},"references-count":10,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2002,11]]}},"alternative-id":["10.1142\/S0219061302000151"],"URL":"https:\/\/doi.org\/10.1142\/s0219061302000151","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,11]]}}}