{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:26:21Z","timestamp":1774628781241,"version":"3.50.1"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T00:00:00Z","timestamp":1618790400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A notion of strictly primitive recursive realizability is introduced by Damnjanovic in 1994. It is a kind of constructive semantics of the arithmetical sentences using primitive recursive functions. It is of interest to study the corresponding predicate logic. It was argued by Park in 2003 that the predicate logic of strictly primitive recursive realizability is not arithmetical. Park\u2019s argument is essentially based on a claim of Damnjanovic that intuitionistic logic is sound with respect to strictly primitive recursive realizability, but that claim was disproved by the author of this article in 2006. The aim of this paper is to present a correct proof of the result of Park.<\/jats:p>","DOI":"10.1017\/s1755020321000174","type":"journal-article","created":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T09:08:00Z","timestamp":1618823280000},"page":"693-721","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["THE NONARITHMETICITY OF THE PREDICATE LOGIC OF STRICTLY PRIMITIVE RECURSIVE REALIZABILITY"],"prefix":"10.1017","volume":"15","author":[{"given":"VALERY","family":"PLISKO","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,4,19]]},"reference":[{"key":"S1755020321000174_r4","doi-asserted-by":"publisher","DOI":"10.2307\/2269016"},{"key":"S1755020321000174_r5","volume-title":"Introduction to Metamathematics","volume":"1","author":"Kleene","year":"1952"},{"key":"S1755020321000174_r3","first-page":"1","article-title":"Some classes of recursive functions","volume":"4","author":"Grzegorczyk","year":"1953","journal-title":"Rozprawy matematyczne"},{"key":"S1755020321000174_r10","unstructured":"[10] Plisko, V. (2007). Primitive Recursive Realizability and Basic Propositional Logic, Utrecht University. Logic Group Preprint Series, Vol. 261, 1\u201327."},{"key":"S1755020321000174_r12","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310032"},{"key":"S1755020321000174_r1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19630090106"},{"key":"S1755020321000174_r6","doi-asserted-by":"publisher","DOI":"10.4064\/cm-6-1-67-78"},{"key":"S1755020321000174_r2","doi-asserted-by":"publisher","DOI":"10.2307\/2275700"},{"key":"S1755020321000174_r11","doi-asserted-by":"publisher","DOI":"10.1070\/IM1977v011n03ABEH001731"},{"key":"S1755020321000174_r7","unstructured":"[7] Park, B. H. (2003). Subrecursive Realizability and Predicate Logic. Ph.D. Thesis, Moscow State University, Russia."},{"key":"S1755020321000174_r9","first-page":"6","article-title":"On the relation between two notions of primitive recursive realizability","volume":"1","author":"Plisko","year":"2006b","journal-title":"Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika"},{"key":"S1755020321000174_r8","doi-asserted-by":"publisher","DOI":"10.1007\/11753728_31"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020321000174","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T01:31:46Z","timestamp":1660699906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020321000174\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,19]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["S1755020321000174"],"URL":"https:\/\/doi.org\/10.1017\/s1755020321000174","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,19]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}