{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T19:24:44Z","timestamp":1759778684597},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2008,1,30]],"date-time":"2008-01-30T00:00:00Z","timestamp":1201651200000},"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":[[2008,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a new axiom scheme for constructive set theory, the Relation Reflection Scheme (RRS). Each instance of this scheme is a theorem of the classical set theory ZF. In the constructive set theory CZF<jats:sup>\u2013<\/jats:sup>, when the axiom scheme is combined with the axiom of Dependent Choices (DC), the result is equivalent to the scheme of Relative Dependent Choices (RDC). In contrast to RDC, the scheme RRS is preserved in Heyting\u2010valued models of CZF<jats:sup>\u2013<\/jats:sup> using set\u2010generated frames. We give an application of the scheme to coinductive definitions of classes. (\u00a9 2008 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710035","type":"journal-article","created":{"date-parts":[[2008,1,30]],"date-time":"2008-01-30T14:16:15Z","timestamp":1201702575000},"page":"5-11","source":"Crossref","is-referenced-by-count":6,"title":["The Relation Reflection Scheme"],"prefix":"10.1002","volume":"54","author":[{"given":"Peter","family":"Aczel","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2008,1,30]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"P.Aczel The type theoretic interpretation of constructive set theory. In: Logic Colloquium '77 (A. MacIntyre L. Pacholski and J. Paris eds.) pp. 55\u201366 (North\u2010Holland 1978).","DOI":"10.1016\/S0049-237X(08)71989-X"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"P.Aczel The type theoretic interpretation of constructive set theory: choice principles. In: The L. E. J. Brouwer Centenary Symposium (S. S. Troelstra and D. van Dalen eds.) pp. 1\u201340 (North\u2010Holland 1982).","DOI":"10.1016\/S0049-237X(09)70120-X"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"P.Aczel The type theoretic interpretation of constructive set theory: inductive definitions. In: Logic Methodology and Philosophy of Science VII (R. B. Marcus et al. eds.) pp. 17\u201349 (North\u2010Holland 1986).","DOI":"10.1016\/S0049-237X(09)70683-4"},{"key":"e_1_2_1_5_2","unstructured":"P.Aczel andM.Rathjen Notes on constructive set theory. Mittag\u2010Leffler Technical Report No. 40 (2001)."},{"key":"e_1_2_1_6_2","unstructured":"N.Gambino Sheaf interpretations for generalised predicative intuitionistic systems. Ph. D. thesis Department of Computer Science University of Manchester (2002)."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.05.021"},{"key":"e_1_2_1_8_2","unstructured":"P.Martin\u2010L\u00f6f Intuitionistic Type Theory. Studies in Proof Theory (Bibliopolis 1984)."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272159"},{"key":"e_1_2_1_10_2","unstructured":"A. S.Troelstra andD.van Dalen Constructivism in Mathematics: An Introduction (two volumes) (North Holland 1988)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710035","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200710035","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T17:52:38Z","timestamp":1699984358000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200710035"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,30]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["10.1002\/malq.200710035"],"URL":"https:\/\/doi.org\/10.1002\/malq.200710035","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1,30]]}}}