{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T23:38:18Z","timestamp":1706053098605},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3663,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We extend an independence result proved in [1]. We show that for all<jats:italic>n<\/jats:italic>, there is a special set of \u03a0<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>sentences {<jats:italic>\u03c6<jats:sub>a<\/jats:sub><\/jats:italic>}<jats:sub><jats:italic>a \u2208 H<\/jats:italic><\/jats:sub>corresponding to elements of a linear ordering (<jats:italic>H, &lt;<jats:sub>H<\/jats:sub><\/jats:italic>) of order type<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200007957_inline1\" \/>. These sentences allow us to build completions {<jats:italic>T<jats:sub>a<\/jats:sub><\/jats:italic>}<jats:sub><jats:italic>a \u2208 H<\/jats:italic><\/jats:sub>of PA such that for<jats:italic>a &lt;<jats:sub>H<\/jats:sub>b, T<jats:sub>a<\/jats:sub><\/jats:italic>\u2229 \u03a3<jats:italic><jats:sub>n<\/jats:sub><\/jats:italic>\u2282<jats:italic>T<jats:sub>b<\/jats:sub><\/jats:italic>\u2229 \u03a3<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, with<jats:italic>\u03c6<jats:sub>a<\/jats:sub><\/jats:italic>\u2208<jats:italic>T<\/jats:italic><jats:sub>a<\/jats:sub>, \u00ac<jats:italic>\u03c6<jats:sub>a<\/jats:sub><\/jats:italic>\u2208<jats:italic>T<jats:sub>h<\/jats:sub><\/jats:italic>. Our method uses the Barwise-Kreisel Compactness Theorem.<\/jats:p>","DOI":"10.2178\/jsl\/1080938820","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:23:28Z","timestamp":1109798608000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Arithmetical independence results using higher recursion theory"],"prefix":"10.1017","volume":"69","author":[{"given":"Andrew","family":"Arana","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200007957_ref007","first-page":"980","volume":"53","author":"Simmons","year":"1988","journal-title":"Large discrete parts of the E-tree"},{"key":"S0022481200007957_ref003","unstructured":"D'Aquino Paola and Knight Julia F. , Coding in I\u03940, 2002, Preprint."},{"key":"S0022481200007957_ref004","first-page":"679","article-title":"Arithmetically definable models of formalizable arithmetic","volume":"5","author":"Feferman","year":"1958","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200007957_ref006","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200007957_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(01)00095-1"},{"key":"S0022481200007957_ref005","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198532132.001.0001","volume-title":"Models of Peano Arithmetic","volume":"15","author":"Kaye","year":"1991"},{"key":"S0022481200007957_ref002","volume-title":"Computable structures and the hyperarithmetical hierarchy","volume":"144","author":"Ash","year":"2000"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200007957","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T22:45:51Z","timestamp":1706049951000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200007957\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,3]]}},"alternative-id":["S0022481200007957"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1080938820","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,3]]}}}