{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:27:26Z","timestamp":1775464046879,"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":17025,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1967,8]]},"abstract":"<jats:p>In this paper it will be shown that the ordering of the recursively enumerable (r.e.) sets under inclusion modulo finite differences (m.f.d.), the ordering of the II1<jats:sup>1<\/jats:sup><jats:sub>1<\/jats:sub> sets under inclusion m.f.d., and the ordering of the metarecursively enumerable (meta-r.e.) sets under inclusion m.f.d. are all distinct. In fact, it will be shown that the three orderings are pairwise elementarily inequivalent when interpreted in the obvious way in a first order language with one binary relation \u201c\u2265.\u201d Our result answers a question of Hartley Rogers, Jr. [3, p. 203]. All necessary background material may be found in [2] and [4].<\/jats:p>","DOI":"10.2307\/2271654","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T16:39:49Z","timestamp":1146933589000},"page":"173-179","source":"Crossref","is-referenced-by-count":19,"title":["Recursion, metarecursion, and inclusion"],"prefix":"10.1017","volume":"32","author":[{"suffix":"Jr.","given":"James C.","family":"Owings","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200113829_ref002","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"},{"key":"S0022481200113829_ref005","unstructured":"Lachlan A. H. , On the lattice of recursively enumerable sets, Transactions of the American Mathematical Society (to appear)."},{"key":"S0022481200113829_ref001","first-page":"309","volume":"23","author":"Friedberg","year":"1958","journal-title":"Three theorems on recursive enumeration"},{"key":"S0022481200113829_ref003","first-page":"190","volume-title":"The theory of models","author":"Kreisel","year":"1965"},{"key":"S0022481200113829_ref004","first-page":"318","volume":"30","author":"Kreisel","year":"1965","journal-title":"Metarecursive sets"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200113829","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T15:57:24Z","timestamp":1559491044000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200113829\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1967,8]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1967,8]]}},"alternative-id":["S0022481200113829"],"URL":"https:\/\/doi.org\/10.2307\/2271654","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1967,8]]}}}