{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T19:03:07Z","timestamp":1648580587878},"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":8320,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:p>The dominical categories were introduced by Di Paola and Heller, as a first step toward a category-theoretic treatment of the generalized first Godel incompleteness theorem [1]. In his Ph.D. dissertation [7], Rosolini subsequently defined the closely related p-categories, which should prove pertinent to category-theoretic representations of incompleteness for intuitionistic systems. The precise relationship between these two concepts is as follows: every dominical category is a pointed p-category, but there are p-categories, indeed pointed p-isotypes (all pairs of objects being isomorphic) with a Turing morphism that are not dominical. The first of these assertions is an easy consequence of the fact that in a dominical category C by definition the near product functor when restricted to the subcategory <jats:italic>C<jats:sub>t<\/jats:sub><\/jats:italic>, of total morphisms of <jats:italic>C<\/jats:italic> (as \u201ctotal\u201d is defined in [1]) constitutes a bona fide product such that the derived associativity and commutativity isomorphisms are natural on <jats:italic>C<\/jats:italic> \u00d7 <jats:italic>C<\/jats:italic> \u00d7 <jats:italic>C<\/jats:italic> and <jats:italic>C<\/jats:italic> \u00d7 <jats:italic>C<\/jats:italic>, respectively, as noted in [7]. As to the second, p-recursion categories (that is, pointed p-isotypes having a Turing morphism) that are not dominical were defined and studied by Montagna in [6], the syntactic p-categories <jats:italic>S<jats:sub>T<\/jats:sub><\/jats:italic> and <jats:italic>S<\/jats:italic>\u2032<jats:sub><jats:italic>T<\/jats:italic><\/jats:sub> associated with consistent, recursively enumerable extensions of Peano arithmetic, PA. These merit detailed investigation on several counts.<\/jats:p>","DOI":"10.2307\/2274707","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:39:41Z","timestamp":1146940781000},"page":"643-660","source":"Crossref","is-referenced-by-count":3,"title":["Some properties of the syntactic p-recursion categories generated by consistent, recursively enumerable extensions of Peano arithmetic."],"prefix":"10.1017","volume":"56","author":[{"given":"Robert A. Di","family":"Paola","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Franco","family":"Montagna","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200024622_ref001","first-page":"594","volume":"52","author":"Di Paola","year":"1987","journal-title":"Dominical categories: recursion theory without elements"},{"key":"S0022481200024622_ref004","first-page":"1252","volume":"55","author":"Heller","year":"1990","journal-title":"An existence theorem for recursion categories"},{"key":"S0022481200024622_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1966-0195722-9"},{"key":"S0022481200024622_ref007","unstructured":"Rosolini G. , Continuity and effectiveness in topoi, D. Phil, dissertation, Merton College, University of Oxford, Oxford, 1986."},{"key":"S0022481200024622_ref005","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870573"},{"key":"S0022481200024622_ref003","doi-asserted-by":"publisher","DOI":"10.4064\/fm-49-1-35-92"},{"key":"S0022481200024622_ref006","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093634998"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200024622","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T17:45:13Z","timestamp":1558115113000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200024622\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["S0022481200024622"],"URL":"https:\/\/doi.org\/10.2307\/2274707","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}