{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T13:15:14Z","timestamp":1772716514141,"version":"3.50.1"},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5064,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1993,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Since in Heyting Arithmetic (HA) all atomic formulas are decidable, a Kripke model for HA may be regarded classically as a collection of classical structures for the language of arithmetic, partially ordered by the submodel relation. The obvious question is then: are these classical structures models of Peano Arithmetic (PA)? And dually: if a collection of models of PA, partially ordered by the submodel relation, is regarded as a Kripke model, is it a model of HA? Some partial answers to these questions were obtained in [6], [3], [1] and [2]. Here we present some results in the same direction, announced in [7]. In particular, it is proved that the classical structures at the nodes of a Kripke model of HA must be models of I\u0394<jats:sub>1<\/jats:sub> (PA<jats:sup>\u2010<\/jats:sup> with induction for provably \u0394<jats:sub>1<\/jats:sub> formulas) and that the relation between these classical structures must be that of a \u0394<jats:sub>1<\/jats:sub>\u2010elementary submodel. MSC: 03F30, 03F55.<\/jats:p>","DOI":"10.1002\/malq.19930390154","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:17:05Z","timestamp":1180199825000},"page":"531-538","source":"Crossref","is-referenced-by-count":10,"title":["On the structure of kripke models of heyting arithmetic"],"prefix":"10.1002","volume":"39","author":[{"given":"Zoran","family":"Markovi\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3466-1_3"},{"key":"e_1_2_1_3_2","unstructured":"Buss S. R. Intuitionistic validity in T\u2010normal Kripke structures. Preprint1991."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093636765"},{"key":"e_1_2_1_5_2","volume-title":"Introduction to Metamathematics","author":"Kleene S. C.","year":"1952"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71685-9"},{"issue":"50","key":"e_1_2_1_7_2","first-page":"3","article-title":"Kripke models for intuitionistic theories with decidable atomic formulas","volume":"36","author":"Markovi Z.","year":"1984","journal-title":"Publ. Inst. Math. Belgrade"},{"key":"e_1_2_1_8_2","first-page":"492","article-title":"On Kripke models for Heyting's arithmetic (abstract)","volume":"51","author":"Markovi\u0107 Z.","year":"1986","journal-title":"J. Symbolic Logic"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"Smorynski C. A. Applications of Kripke models. In [10] pp.324\u2013391.","DOI":"10.1007\/BFb0066744"},{"key":"e_1_2_1_10_2","first-page":"459","volume-title":"Centenary Symposium","author":"Smorynski C. A.","year":"1982"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066739"},{"key":"e_1_2_1_12_2","volume-title":"Constructivism in Mathematics","author":"Troelstra A. S.","year":"1988"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19930390154","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19930390154","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T21:01:32Z","timestamp":1698267692000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19930390154"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,1]]}},"alternative-id":["10.1002\/malq.19930390154"],"URL":"https:\/\/doi.org\/10.1002\/malq.19930390154","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,1]]}}}