{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T21:31:28Z","timestamp":1695850288350},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8958,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1989,9]]},"abstract":"<jats:p>Recursion categories have been proposed by Di Paola and Heller in [DPH] as the basis for a category-theoretic approach to recursion theory, in the context of a more general and ambitious project of a purely algebraic treatment of incompleteness phenomena. The way in which the classical notion of creative set is rendered in this new category-theoretic framework plays, therefore, a central role. This is done in [DPH] (Definition 8.1) by defining the notion of <jats:italic>creative domains<\/jats:italic> or, rather, domains which are creative <jats:italic>relative to some criterion:<\/jats:italic> thus, in a recursion category, every criterion provides a notion of creativeness.<\/jats:p><jats:p>A basic result on creative domains (cf. [DPH, Theorem 8.13]) is that, under certain assumptions, a version of the classical result, due to Myhill [MYH], stating that every creative set is complete, holds: in a recursion category with equality (i.e. <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200041724_inline1\" \/> exists for every object X) and having enough atoms, every domain which is creative with respect to atoms is also complete.<\/jats:p>","DOI":"10.2307\/2274763","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:31:33Z","timestamp":1146940293000},"page":"1023-1041","source":"Crossref","is-referenced-by-count":3,"title":["Creativeness and completeness in recursion categories of partial recursive operators"],"prefix":"10.1017","volume":"54","author":[{"given":"Franco","family":"Montagna","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Sorbi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200041724_ref006","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200041724_ref005","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19550010205"},{"key":"S0022481200041724_ref007","unstructured":"Wadge W. W. , Reducibility and determinateness on the Baire space, Ph.D. thesis, University of California, Berkeley, California, 1984."},{"key":"S0022481200041724_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9839-7"},{"key":"S0022481200041724_ref002","first-page":"594","volume":"52","author":"Di Paola","year":"1987","journal-title":"Dominical categories: recursion theory without elements"},{"key":"S0022481200041724_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12898-5"},{"key":"S0022481200041724_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1958-0097310-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200041724","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T15:52:25Z","timestamp":1558281145000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200041724\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1989,9]]}},"alternative-id":["S0022481200041724"],"URL":"https:\/\/doi.org\/10.2307\/2274763","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,9]]}}}