{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T20:20:34Z","timestamp":1775506834246,"version":"3.50.1"},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11424,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0\u2032. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice \u2130 of recursively enumerable sets with inclusion. We introduce the notion of a promptly simple set. This describes the essential feature of r.e. generic sets with respect to automorphism constructions.<\/jats:p>","DOI":"10.2307\/2273100","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:01:43Z","timestamp":1146938503000},"page":"809-823","source":"Crossref","is-referenced-by-count":33,"title":["Recursively enumerable generic sets"],"prefix":"10.1017","volume":"47","author":[{"given":"Wolfgang","family":"Maass","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200043681_ref006","unstructured":"Soare R. I. , Automorphisms of the lattice of recursively enumerable sets. Part II. Low sets (to appear)."},{"key":"S0022481200043681_ref001","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200043681_ref005","first-page":"545","volume":"42","author":"Soare","year":"1977","journal-title":"Computational complexity, speedable and levelable sets"},{"key":"S0022481200043681_ref003","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200043681_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/1970842"},{"key":"S0022481200043681_ref002","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1980.87.135"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200043681","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T16:18:41Z","timestamp":1558714721000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200043681\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["S0022481200043681"],"URL":"https:\/\/doi.org\/10.2307\/2273100","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}