{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T22:58:36Z","timestamp":1773097116844,"version":"3.50.1"},"reference-count":16,"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":2933,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2006,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov's principle but meshes well with some classical principles, including the lesser limited principle of omniscience and weak K\u00f6nig's lemma. We discuss some applications, as well as some previous results in the literature.<\/jats:p>","DOI":"10.2178\/jsl\/1140641178","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:22:31Z","timestamp":1198081351000},"page":"329-346","source":"Crossref","is-referenced-by-count":14,"title":["Bounded modified realizability"],"prefix":"10.1017","volume":"71","author":[{"given":"Fernando","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"Ana","family":"Nunes","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200006502_ref015","first-page":"217","volume-title":"Kurt G\u00f6del collected works","volume":"II","author":"Troelstra","year":"1990"},{"key":"S0022481200006502_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066739"},{"key":"S0022481200006502_ref010","first-page":"1218","volume":"63","author":"Kohlenbach","year":"1998","journal-title":"Relative constructivity"},{"key":"S0022481200006502_ref008","first-page":"109","volume":"10","author":"Kleene","year":"1945","journal-title":"On the interpretation of intuitionistic number theory"},{"key":"S0022481200006502_ref006","doi-asserted-by":"publisher","DOI":"10.1111\/j.1746-8361.1958.tb01464.x"},{"key":"S0022481200006502_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(01)00077-X"},{"key":"S0022481200006502_ref003","first-page":"652","volume":"50","author":"Bezem","year":"1985","journal-title":"Strongly majorizable functional of finite type: a model for bar recursion containing discontinuous Junctionals"},{"key":"S0022481200006502_ref013","first-page":"139","volume":"27","author":"Kreisel","year":"1962","journal-title":"On weak completeness of intuitionistic predicate logic"},{"key":"S0022481200006502_ref012","first-page":"136","article-title":"Proof mining: a systematic way of analysing proofs in mathematics","volume":"242","author":"Kohlenbach","year":"2003","journal-title":"Proceedings of the Steklov Institute of Mathematics"},{"key":"S0022481200006502_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80020-7"},{"key":"S0022481200006502_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050055"},{"key":"S0022481200006502_ref007","first-page":"454","volume-title":"Metamathematical investigation of intuitionistic Arithmetic and Analysis","volume":"344","author":"Howard","year":"1973"},{"key":"S0022481200006502_ref001","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1109\/LICS.2004.1319613","volume-title":"Proceedings of the 19th annual IEEE symposium on logic and computer science","volume":"117","author":"Akama","year":"2004"},{"key":"S0022481200006502_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80021-9"},{"key":"S0022481200006502_ref004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565663"},{"key":"S0022481200006502_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.11.001"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200006502","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T10:30:31Z","timestamp":1684146631000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200006502\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,3]]}},"alternative-id":["S0022481200006502"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1140641178","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3]]}}}