{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T00:06:35Z","timestamp":1699920395528},"reference-count":8,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2010,11,9]],"date-time":"2010-11-09T00:00:00Z","timestamp":1289260800000},"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":[[2010,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the article [4], a new constructive set theoretic principle called Refinement was introduced and analysed. While it seemed to be significantly weaker than its alternative, the more established axiom of Fullness (a constructive version of the Powerset axiom from classical set theory), it was shown to suffice to imply many of the mathematically important consequences. In this article, we will define for each set <jats:italic>A<\/jats:italic> a set of truth values which measures the complexity of the equality relation on <jats:italic>A<\/jats:italic>. Using these sets we will show that Refinement is actually equivalent to Fullness on the basis of the other axioms of constructive Zermelo\u2010Fraenkel set theory (\u00a9 2010 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200910115","type":"journal-article","created":{"date-parts":[[2010,11,9]],"date-time":"2010-11-09T08:34:48Z","timestamp":1289291688000},"page":"666-669","source":"Crossref","is-referenced-by-count":0,"title":["Refinement is equivalent to Fullness"],"prefix":"10.1002","volume":"56","author":[{"given":"Albert","family":"Ziegler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,11,9]]},"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 Studies in Logic and the Foundation of Mathematics (A. Macintyre L. Pacholski and J. Paris eds.) pp. 55\u201366 (North\u2013Holland 1978).","DOI":"10.1016\/S0049-237X(08)71989-X"},{"key":"e_1_2_1_3_2","unstructured":"P.Aczel andM.Rathjen Notes on Constructive Set Theory. Institut Mittag\u2013Leffler Preprint 40 2000\/01 (2000)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-9014-9"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1122038923"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11813-007-0005-6"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272159"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1129642124"},{"key":"e_1_2_1_9_2","unstructured":"A.Ziegler Some reflections about the principle of Image Collection. In: Logical Advances to Computational Barriers (A. Beckmann U. Berger B. L\u00f6we and J. V. Tucker eds.) University of Wales Swansea Report Series pp. 282\u2013288 (2006)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200910115","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200910115","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200910115","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T18:04:36Z","timestamp":1699898676000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200910115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,9]]},"references-count":8,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["10.1002\/malq.200910115"],"URL":"https:\/\/doi.org\/10.1002\/malq.200910115","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11,9]]}}}