{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T09:03:26Z","timestamp":1750323806875},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,1,15]],"date-time":"2010-01-15T00:00:00Z","timestamp":1263513600000},"content-version":"vor","delay-in-days":14,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present a refinement ofthe bounded modified realizability which provides both upper and lower bounds for witnesses. Our interpretation is based on a generalisation of Howard\/Bezem's notion of strong majorizability. We show how the bounded modified realizability coincides with (a weak version of) our interpretation in the case when least elements exist (e.g. natural numbers). The new interpretation, however, permits the extraction of more accurate bounds, and provides an ideal setting for dealing directly with data types whose natural ordering is not well\u2010founded (\u00a9 2010 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200810029","type":"journal-article","created":{"date-parts":[[2010,1,15]],"date-time":"2010-01-15T18:25:16Z","timestamp":1263579916000},"page":"13-28","source":"Crossref","is-referenced-by-count":3,"title":["Confined modified realizability"],"prefix":"10.1002","volume":"56","author":[{"given":"Gilda","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"Paulo","family":"Oliva","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,1,15]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274319"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/421098"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00097-8"},{"key":"e_1_2_1_5_2","unstructured":"F.Ferreira Proofinterpretations and majorizability. To appear in: Proceedings ofthe Logic Colloquium 2007."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1140641178"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.11.001"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2006.07.002"},{"key":"e_1_2_1_9_2","unstructured":"A. E.Ingham The Distribution of Prime Numbers (Cambridge Mathematical Library 1932)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2269016"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01794980"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.2307\/2586648"},{"key":"e_1_2_1_13_2","unstructured":"U.Kohlenbach Applied Proof Theory: ProofInterpretations and their Use in Mathematics. (Springer 2008)."},{"key":"e_1_2_1_14_2","unstructured":"G.Kreisel Interpretation of analysis by means ofconstructive functionals offinite types. In: Constructivity in Mathematics (A. Heyting ed.) pp. 101\u2013128. (North Holland 1959)."},{"key":"e_1_2_1_15_2","unstructured":"C.Papadimitriou Computational Complexity (Addison\u2010Wesley 1994)."},{"key":"e_1_2_1_16_2","doi-asserted-by":"crossref","unstructured":"A. S.Troelstra Realizability. In: Handbook of Proof Theory (S. R. Buss ed.) pp. 408\u2013473 (North Holland 1998).","DOI":"10.1016\/S0049-237X(98)80021-9"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200810029","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200810029","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T12:35:46Z","timestamp":1700570146000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200810029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1002\/malq.200810029"],"URL":"https:\/\/doi.org\/10.1002\/malq.200810029","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}