{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:52:47Z","timestamp":1759146767627,"version":"3.37.3"},"reference-count":17,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2016,12,7]],"date-time":"2016-12-07T00:00:00Z","timestamp":1481068800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PEst\u2010OE\/MAT\/UI0209\/2011","SFRH\/BPD\/97436\/2013"],"award-info":[{"award-number":["PEst\u2010OE\/MAT\/UI0209\/2011","SFRH\/BPD\/97436\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p>We show how to interpret weak K\u0151nig's lemma in some recently defined theories of nonstandard arithmetic in all finite types. Two types of interpretations are described, with very different verifications. The celebrated conservation result of Friedman's about weak K\u0151nig's lemma can be proved using these interpretations. We also address some issues concerning the collecting of witnesses in herbrandized functional interpretations.<\/jats:p>","DOI":"10.1002\/malq.201600066","type":"journal-article","created":{"date-parts":[[2016,12,7]],"date-time":"2016-12-07T13:02:23Z","timestamp":1481115743000},"page":"114-123","source":"Crossref","is-referenced-by-count":3,"title":["Interpreting weak K\u0151nig's lemma in theories of nonstandard arithmetic"],"prefix":"10.1002","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2143-3289","authenticated-orcid":false,"given":"Bruno","family":"Dinis","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Faculdade de Ci\u00eancias da Universidade de Lisboa Campo Grande Edif\u00edcio\u00a0C6 1749\u2010016\u00a0Lisboa Portugal"}]},{"given":"Fernando","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Faculdade de Ci\u00eancias da Universidade de Lisboa Campo Grande Edif\u00edcio\u00a0C6 1749\u2010016\u00a0Lisboa Portugal"}]}],"member":"311","published-online":{"date-parts":[[2016,12,7]]},"reference":[{"key":"e_1_2_7_2_1","first-page":"19","volume-title":"Lecture Notes in Logic Vol. 21","author":"Avigad J.","year":"2005"},{"key":"e_1_2_7_3_1","unstructured":"J.Avigad Review of [7] Mathematical Reviews MR3325571 2016."},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80020-7"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.2307\/2274319"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.09.004"},{"key":"e_1_2_7_7_1","article-title":"A functional interpretation of classical logic","author":"Ferreira F.","year":"2016","journal-title":"manuscript"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2015.02.001"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.11.001"},{"key":"e_1_2_7_10_1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198532132.001.0001","volume-title":"Models of Peano Arithmetic","author":"Kaye R.","year":"1991"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275367"},{"volume-title":"Applied Proof Theory: Proof Interpretations and their Use in Mathematics","year":"2008","author":"Kohlenbach U.","key":"e_1_2_7_12_1"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1977-14398-X"},{"volume-title":"Mathematical Logic","year":"1967","author":"Shoenfield J. 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