{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T11:43:14Z","timestamp":1648640594238},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":923,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2011,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a natural strengthening of prompt simplicity which we call strong promptness, and study its relationship with existing lowness classes. This notion provides a \u2264<jats:sub><jats:italic>wtt<\/jats:italic><\/jats:sub> version of superlow cuppability. We show that every strongly prompt c.e. set is superlow cuppable. Unfortunately, strong promptness is not a Turing degree notion, and so cannot characterize the sets which are superlow cuppable. However, it is a wtt-degree notion, and we show that it characterizes the degrees which satisfy a wtt-degree notion very close to the definition of superlow cuppability.<\/jats:p><jats:p>Further, we study the strongly prompt c.e. sets in the context of other notions related promptness, superlowness, and cupping. In particular, we show that every benign cost function has a strongly prompt set which obeys it, providing an analogue to the known result that every cost function with the limit condition has a prompt set which obeys it. We also study the effect that lowness properties have on the behaviour of a set under the join operator. In particular we construct an array noncomputable c.e. set whose join with every low c.e. set is low.<\/jats:p>","DOI":"10.2178\/jsl\/1309952528","type":"journal-article","created":{"date-parts":[[2011,7,6]],"date-time":"2011-07-06T07:42:35Z","timestamp":1309938155000},"page":"946-972","source":"Crossref","is-referenced-by-count":0,"title":["Strengthening prompt simplicity"],"prefix":"10.1017","volume":"76","author":[{"given":"David","family":"Diamondstone","sequence":"first","affiliation":[]},{"given":"Keng Meng","family":"Ng","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200001602_ref004","first-page":"881","volume":"66","author":"Cholak","year":"2001","journal-title":"An almost deep degree"},{"key":"S0022481200001602_ref013","unstructured":"Ng K. M. , Beyond strong jump traceablility, Proceedings of the London Mathematical Society , (to appear)."},{"key":"S0022481200001602_ref007","first-page":"103","volume-title":"Trivial reals, Proceedings of the 7th and 8th Asian Logic Conferences","author":"Downey","year":"2003"},{"key":"S0022481200001602_ref012","unstructured":"Ng K. M. , Computability, traceability and beyond, Ph.D. Dissertation, Victoria University of Wellington, 2009."},{"key":"S0022481200001602_ref006","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061307000640"},{"key":"S0022481200001602_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511629167.005"},{"key":"S0022481200001602_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1983-0704618-2"},{"key":"S0022481200001602_ref002","volume-title":"Lowness properties of r.e. sets","author":"Bickford","year":"1982"},{"key":"S0022481200001602_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2004.10.006"},{"key":"S0022481200001602_ref015","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199230761.001.0001"},{"key":"S0022481200001602_ref005","first-page":"1264","volume":"74","author":"Diamondstone","year":"2009","journal-title":"Promptness does not imply superlow cuppability"},{"key":"S0022481200001602_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1984-0719661-8"},{"key":"S0022481200001602_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2007.09.008"},{"key":"S0022481200001602_ref009","first-page":"45","article-title":"Lowness properties and approximations of the jump","volume":"143","author":"Figueira","year":"2006","journal-title":"Proceedings of the twelfth Workshop on Logic, Language, Information and Computation (WoLLIC 2005)"},{"key":"S0022481200001602_ref010","unstructured":"Greenberg N. and Nies A. , Benign cost functions and lowness properties, to appear."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200001602","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T01:56:16Z","timestamp":1556330176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200001602\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["S0022481200001602"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1309952528","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9]]}}}