{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T17:55:46Z","timestamp":1711994146015},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T00:00:00Z","timestamp":1540252800000},"content-version":"unspecified","delay-in-days":52,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2018,9]]},"abstract":"Abstract<\/jats:title>BON+<\/jats:sup> is an applicative theory and closely related to the first order parts of the standard systems of explicit mathematics. As such it is also a natural framework for abstract computations. In this article we analyze this aspect of BON+<\/jats:sup> more closely. First a point is made for introducing a new operation \u03c4<\/jats:italic>N<\/jats:sub>, called truncation, to obtain a natural formalization of partial recursive functions in our applicative framework. Then we introduce the operational versions of a series of notions that are all equivalent to semi-decidability in ordinary recursion theory on the natural numbers, and study their mutual relationships over BON+<\/jats:sup> with \u03c4<\/jats:italic>N<\/jats:sub>.<\/jats:p>","DOI":"10.1017\/jsl.2018.34","type":"journal-article","created":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T07:16:27Z","timestamp":1540278987000},"page":"967-990","source":"Crossref","is-referenced-by-count":2,"title":["TRUNCATION AND SEMI-DECIDABILITY NOTIONS IN APPLICATIVE THEORIES"],"prefix":"10.1017","volume":"83","author":[{"given":"GERHARD","family":"J\u00c4GER","sequence":"first","affiliation":[]},{"given":"TIMOTEJ","family":"ROSEBROCK","sequence":"additional","affiliation":[]},{"given":"SATO","family":"KENTARO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,10,23]]},"reference":[{"key":"S0022481218000348_ref1","volume-title":"The Lambda Calculus: Its Syntax and Semantics","author":"Barendregt","year":"1985"},{"key":"S0022481218000348_ref17","unstructured":"[17] Rosebrock T. , Some models and semi-decidability notions of applicative theories, Ph.D. thesis, in preparation."},{"key":"S0022481218000348_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0062852"},{"key":"S0022481218000348_ref18","volume-title":"Constructivism in Mathematics, I","volume":"vol. 121","author":"Troelstra","year":"1988"},{"key":"S0022481218000348_ref14","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200710081"},{"key":"S0022481218000348_ref4","first-page":"159","volume-title":"Logic Colloquium \u201978","volume":"vol. 97","author":"Feferman","year":"1979"},{"key":"S0022481218000348_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68952-9"},{"key":"S0022481218000348_ref19","volume-title":"Constructivism in Mathematics, II","volume":"vol. 123","author":"Troelstra","year":"1988"},{"key":"S0022481218000348_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050007"},{"key":"S0022481218000348_ref8","volume-title":"Applikative Theorien und Frege-Strukturen","author":"Kahle","year":"1997"},{"key":"S0022481218000348_ref6","unstructured":"[6] Feferman S. , J\u00e4ger G. , and Strahm T. , Foundations of explicit mathematics, in preparation."},{"key":"S0022481218000348_ref15","unstructured":"[15] Nemoto T. and Sato K. , A marriage of Brouwer\u2019s Intuitionism and Hilbert\u2019s Finitism I: Arithmetic, this JOURNAL, accepted for publication."},{"key":"S0022481218000348_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12898-5"},{"key":"S0022481218000348_ref10","volume-title":"The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings","author":"Kanamori","year":"2003"},{"key":"S0022481218000348_ref13","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/pdr022"},{"key":"S0022481218000348_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90013-4"},{"key":"S0022481218000348_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0071692"},{"key":"S0022481218000348_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-47992-6"},{"key":"S0022481218000348_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020316000095"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481218000348","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T17:10:33Z","timestamp":1555175433000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481218000348\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["S0022481218000348"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2018.34","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9]]}}}