{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T09:56:47Z","timestamp":1772445407990,"version":"3.50.1"},"reference-count":5,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8685,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce the notion of \u201csemi-r.e.\u201d for subsets of <jats:italic>\u03c9<\/jats:italic>, a generalization of \u201csemirecursive\u201d and of \u201cr.e.\u201d, and the notion of \u201cweakly semirecursive\u201d, a generalization of \u201csemi-r.e.\u201d. We show that <jats:italic>A<\/jats:italic> is weakly semirecursive iff, for any <jats:italic>n<\/jats:italic> numbers <jats:italic>x<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026,<jats:italic>x<jats:sub>n<\/jats:sub><\/jats:italic>, knowing how many of these numbers belong to <jats:italic>A<\/jats:italic> is equivalent to knowing which of these numbers belong to <jats:italic>A<\/jats:italic>. It is shown that there exist weakly semirecursive sets that are neither semi-r.e. nor co-semi-r.e. On the other hand, we exhibit nonzero Turing degrees in which every weakly semirecursive set is semirecursive. We characterize the notion \u201c<jats:italic>A<\/jats:italic> is weakly semirecursive and recursive in <jats:italic>K<\/jats:italic>\u201d in terms of recursive approximations to <jats:italic>A<\/jats:italic>. We also show that if a finite Boolean combination of r.e. sets is semirecursive then it must be r.e. or co-r.e. Several open questions are raised.<\/jats:p>","DOI":"10.2307\/2274653","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"637-644","source":"Crossref","is-referenced-by-count":13,"title":["Weakly semirecursive sets"],"prefix":"10.1017","volume":"55","author":[{"suffix":"Jr.","given":"Carl G.","family":"Jockusch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"suffix":"Jr.","given":"James C.","family":"Owings","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200026037_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200026037_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1968-0220595-7"},{"key":"S0022481200026037_ref001","volume-title":"Information and Computation","author":"Beigel"},{"key":"S0022481200026037_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90010-9"},{"key":"S0022481200026037_ref004","first-page":"761","volume":"54","author":"Owings","year":"1989","journal-title":"A cardinality version of Beigel's nonspeedup theorem"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200026037","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:13:10Z","timestamp":1558213990000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200026037\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200026037"],"URL":"https:\/\/doi.org\/10.2307\/2274653","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}