{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T15:57:00Z","timestamp":1721923020169},"reference-count":19,"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":5215,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1999,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We investigate the modal logic of interpretability over Peano arithmetic. Our main result is a compactness theorem that extends the arithmetical completeness theorem for the interpretability logic ILM<jats:sup>\u03c9<\/jats:sup>. This extension concerns recursively enumerable sets of formulas of interpretability logic (rather than single formulas). As corollaries we obtain a uniform arithmetical completeness theorem for the interpretability logic ILM and a partial answer to a question of Orey from 1961. After some simplifications, we also obtain Shavrukov's embedding theorem for Magari algebras (a.k.a. diagonalizable algebras).<\/jats:p>","DOI":"10.2307\/2586787","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:03:57Z","timestamp":1146938637000},"page":"1407-1425","source":"Crossref","is-referenced-by-count":3,"title":["Interpretability over peano arithmetic"],"prefix":"10.1017","volume":"64","author":[{"given":"Claes","family":"Stranneg\u00e5rd","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200012652_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02121661"},{"key":"S0022481200012652_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8601-8"},{"key":"S0022481200012652_ref001","first-page":"1059","volume":"55","author":"Berarducci","year":"1990","journal-title":"The interpretability logic of Peano arithmetic"},{"key":"S0022481200012652_ref016","doi-asserted-by":"crossref","unstructured":"Visser A. , Interpretability logic, [8], 1990, pp. 175\u2013209.","DOI":"10.1007\/978-1-4613-0609-2_13"},{"key":"S0022481200012652_ref009","volume-title":"Technical Report 5","author":"Shavrukov","year":"1988"},{"key":"S0022481200012652_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19610070710"},{"key":"S0022481200012652_ref005","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198532132.001.0001","volume-title":"Models of Peano arithmetic","author":"Kaye","year":"1991"},{"key":"S0022481200012652_ref004","volume-title":"Handbook of proof theory","author":"Japartdze","year":"1998"},{"key":"S0022481200012652_ref012","first-page":"79","volume":"62","author":"Shavrukov","year":"1997","journal-title":"Undecidability of diagonalizable algebras"},{"key":"S0022481200012652_ref018","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093634485"},{"key":"S0022481200012652_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757006"},{"key":"S0022481200012652_ref003","volume-title":"Metamathematics of first-order arithmetic","author":"H\u00e1jek","year":"1991"},{"key":"S0022481200012652_ref008","volume-title":"Mathematical logic, Proceedings of the Heyting 1988 summer school in Varna, Bulgaria","author":"Petkov","year":"1990"},{"key":"S0022481200012652_ref002","doi-asserted-by":"crossref","unstructured":"de Jongh D. and Veltman F. , Provability logics for relative interpretability, [8], 1990, pp. 31\u201342.","DOI":"10.1007\/978-1-4613-0609-2_3"},{"key":"S0022481200012652_ref011","article-title":"Subalgebras of diagonalizable algebras of theories containing arithmetic","volume":"CCCXXIII","author":"Shavrukov","year":"1993","journal-title":"Dissertationes mathematicae (Rozprawy matematycne)"},{"key":"S0022481200012652_ref015","unstructured":"Stranneg\u00e5rd C. , Arithmetical realizations of modal formulas, Ph.D. thesis , University of G\u00f6teborg, 1997."},{"key":"S0022481200012652_ref017","volume-title":"Technical Report LGPS 174","author":"Visser","year":"1997"},{"key":"S0022481200012652_ref019","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1040609301"},{"key":"S0022481200012652_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90202-O"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200012652","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T07:19:55Z","timestamp":1707031195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200012652\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,12]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1999,12]]}},"alternative-id":["S0022481200012652"],"URL":"https:\/\/doi.org\/10.2307\/2586787","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,12]]}}}