{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T01:36:48Z","timestamp":1648690608068},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1472,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the connection between Schnorr triviality and genericity. We show that while no 2-generic is Turing equivalent to a Schnorr trivial and no 1-generic is <jats:italic>tt<\/jats:italic>-equivalent to a Schnorr trivial, there is a 1-generic that is Turing equivalent to a Schnorr trivial. However, every such 1-generic must be high. As a corollary, we prove that not all <jats:italic>K<\/jats:italic>-trivials are Schnorr trivial. We also use these techniques to extend a previous result and show that the bases of cones of Schnorr trivial Turing degrees are precisely those whose jumps are at least 0\u2033.<\/jats:p>","DOI":"10.2178\/jsl\/1264433915","type":"journal-article","created":{"date-parts":[[2010,1,25]],"date-time":"2010-01-25T10:38:59Z","timestamp":1264415939000},"page":"191-207","source":"Crossref","is-referenced-by-count":5,"title":["Schnorr triviality and genericity"],"prefix":"10.1017","volume":"75","author":[{"given":"Johanna N.Y.","family":"Franklin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002899_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-007-0061-3"},{"key":"S0022481200002899_ref001","doi-asserted-by":"publisher","DOI":"10.1145\/321892.321894"},{"key":"S0022481200002899_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2004.10.006"},{"key":"S0022481200002899_ref014","volume-title":"On sequences with simple initial segments","author":"Zambella","year":"1990"},{"key":"S0022481200002899_ref002","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310121"},{"key":"S0022481200002899_ref003","doi-asserted-by":"publisher","DOI":"10.2178\/bsl\/1154698741"},{"key":"S0022481200002899_ref004","doi-asserted-by":"publisher","DOI":"10.1142\/9789812705815_0005"},{"key":"S0022481200002899_ref005","first-page":"533","volume":"69","author":"Downey","year":"2004","journal-title":"Schnorr randomness"},{"key":"S0022481200002899_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0112458"},{"key":"S0022481200002899_ref007","volume-title":"Schnorr trivial sets and truth-table reducibility","author":"Franklin","year":"2008"},{"key":"S0022481200002899_ref011","volume-title":"Classical recursion theory. Volume II","volume":"143","author":"Odifreddi","year":"1999"},{"key":"S0022481200002899_ref008","first-page":"677","volume":"57","author":"Kummer","year":"1992","journal-title":"A proof of Beigel's cardinality conjecture"},{"key":"S0022481200002899_ref009","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19660120125"},{"key":"S0022481200002899_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002899","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,28]],"date-time":"2019-04-28T16:37:35Z","timestamp":1556469455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002899\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["S0022481200002899"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1264433915","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3]]}}}