{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T15:42:50Z","timestamp":1775403770240,"version":"3.50.1"},"reference-count":7,"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":284,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A generic computation of a subset <jats:italic>A<\/jats:italic> of \u2115 consists of a computation that correctly computes <jats:italic>most<\/jats:italic> of the bits of <jats:italic>A<\/jats:italic>, and never incorrectly computes any bits of <jats:italic>A<\/jats:italic>, but which does not necessarily give an answer for every input. The motivation for this concept comes from group theory and complexity theory, but the purely recursion theoretic analysis proves to be interesting, and often counterintuitive. The primary result of this paper is that there are no minimal pairs for generic computability, answering a question of Jockusch and Schupp.<\/jats:p>","DOI":"10.2178\/jsl.7802090","type":"journal-article","created":{"date-parts":[[2013,5,15]],"date-time":"2013-05-15T14:11:08Z","timestamp":1368627068000},"page":"511-522","source":"Crossref","is-referenced-by-count":12,"title":["Nonexistence of minimal pairs for generic computability"],"prefix":"10.1017","volume":"78","author":[{"given":"Gregory","family":"Igusa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200000116_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00167-4"},{"key":"S0022481200000116_ref006","doi-asserted-by":"publisher","DOI":"10.1137\/0215020"},{"key":"S0022481200000116_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200000116_ref002","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exn101"},{"key":"S0022481200000116_ref001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061313500050"},{"key":"S0022481200000116_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(91)90007-R"},{"key":"S0022481200000116_ref004","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/jdr051"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000116","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T21:40:01Z","timestamp":1556055601000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000116\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["S0022481200000116"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7802090","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6]]}}}