{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T07:13:16Z","timestamp":1697699596577},"reference-count":6,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,5,18]],"date-time":"2007-05-18T00:00:00Z","timestamp":1179446400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with (homo)morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms (including \u22a4 and \u22a5) using \u2227, \u2228, \u2200, and \u2192, with the restriction that antecedents of \u2192 must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model\u2010consistency theorem: The universal fragment of a theory \u0393 is contained in the universal fragment of a theory \u0394 if and only if every rooted Kripke model of \u0394 is strongly equivalent to a submodel of a rooted Kripke model of \u0393. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (\u00a9 2007 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200610048","type":"journal-article","created":{"date-parts":[[2007,5,18]],"date-time":"2007-05-18T22:45:15Z","timestamp":1179528315000},"page":"311-320","source":"Crossref","is-referenced-by-count":9,"title":["Kripke submodels and universal sentences"],"prefix":"10.1002","volume":"53","author":[{"given":"Ben","family":"Ellison","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Fleischmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dan","family":"McGinn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wim","family":"Ruitenburg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,5,18]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310052"},{"key":"e_1_2_1_3_2","unstructured":"D.van Dalen Logic and Structure (4th ed.). Universitext (Springer 2004)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"J.Hirschfeld andW. H.Wheeler Forcing Arithmetic Division Rings. Lecture Notes in Mathematics 454 (Springer 1975).","DOI":"10.1007\/BFb0064082"},{"key":"e_1_2_1_5_2","unstructured":"W.Hodges Model Theory. Encyclopedia of Mathematics and its Applications 42 (Cambridge University Press 1993)."},{"key":"e_1_2_1_6_2","unstructured":"A. S.Troelstra andD.van Dalen Constructivism in Mathematics An Introduction (Vol. 1). Studies in Logic and the Foundations of Mathematics 121 (North\u2010Holland 1988)."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/PL00003842"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200610048","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200610048","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T15:05:18Z","timestamp":1697641518000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200610048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,18]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["10.1002\/malq.200610048"],"URL":"https:\/\/doi.org\/10.1002\/malq.200610048","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5,18]]}}}