{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T15:55:32Z","timestamp":1713196532888},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5064,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1993,1]]},"abstract":"Abstract<\/jats:title>We study the degrees of unsolvability of sets which are cohesive (or have weaker recursion\u2010theoretic \u201csmallness\u201d properties). We answer a question raised by the first author in 1972 by showing that there is a cohesive set A<\/jats:italic> whose degree a satisfies a' = 0\u2033 and hence is not high. We characterize the jumps of the degrees of r\u2010cohesive sets, and we show that the degrees of r\u2010cohesive sets coincide with those of the cohesive sets. We obtain analogous results for strongly hyperimmune and strongly hyperhyperimmune sets in place of r\u2010cohesive and cohesive sets, respectively. We show that every strongly hyperimmune set whose degree contains either a Boolean combination of \u22112 sets or a 1\u2010generic set is of high degree. We also study primitive recursive analogues of these notions and in this case we characterize the corresponding degrees exactly. MSC: 03D30, 03D55.<\/jats:p>","DOI":"10.1002\/malq.19930390153","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:17:13Z","timestamp":1180199833000},"page":"515-530","source":"Crossref","is-referenced-by-count":44,"title":["A cohesive set which is not high"],"prefix":"10.1002","volume":"39","author":[{"given":"Carl","family":"Jockusch","sequence":"first","affiliation":[]},{"given":"Frank","family":"Stephan","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272750"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"Fortnow L. W.Gasarch S.Jain E.Kinber M.Kummer S.Kurtz M.Pleszkoch T.Slaman R.Solovay andF.Stephan Extremes in the degrees of inferability. Manuscript 1993.","DOI":"10.1016\/0168-0072(94)90035-3"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2270912"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1972-113-9"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02787575"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)70045-4"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/1996261"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274816"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274273"},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BFb0076224","volume-title":"Recursion Theory Week, Proceedings","author":"Ku\u010dera A.","year":"1985"},{"key":"e_1_2_1_12_2","first-page":"219","volume-title":"Proceedings, Logic Colloquium '87","author":"Ku\u010dera A.","year":"1989"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19660120125"},{"key":"e_1_2_1_14_2","volume-title":"Classical Recursion Theory","author":"Odifreddi P.","year":"1989"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.2307\/2273221"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19930390153","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19930390153","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T21:01:27Z","timestamp":1698267687000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19930390153"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,1]]}},"alternative-id":["10.1002\/malq.19930390153"],"URL":"https:\/\/doi.org\/10.1002\/malq.19930390153","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,1]]}}}