{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T08:41:52Z","timestamp":1708677712798},"reference-count":15,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2008,3,7]],"date-time":"2008-03-07T00:00:00Z","timestamp":1204848000000},"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":[[2008,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A weak form of intuitionistic set theory<jats:bold>WST<\/jats:bold>lacking the axiom of extensionality is introduced. While<jats:bold>WST<\/jats:bold>is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up<jats:bold>WST<\/jats:bold>with moderate extensionality principles or quotient sets enables the derivation to go through. (\u00a9 2008 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710030","type":"journal-article","created":{"date-parts":[[2008,3,7]],"date-time":"2008-03-07T08:44:58Z","timestamp":1204879498000},"page":"194-201","source":"Crossref","is-referenced-by-count":3,"title":["The axiom of choice and the law of excluded middle in weak set theories"],"prefix":"10.1002","volume":"54","author":[{"given":"John L.","family":"Bell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2008,3,7]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"P.Aczel andM.Rathjen Notes on constructive set theory. Institut Mittag\u2010Lef. er Report 40 2000\/2001. Available on http:\/\/www.ml.kva.se\/preprints\/meta\/AczelMon_Sep_24_09_16_56.rdf.html."},{"key":"e_1_2_1_3_2","unstructured":"J. L.Bell Toposes and Local Set Theories: An Introduction (Clarendon Press 1988). To be republished by Dover in 2008."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1090\/S0002-9939-1975-0373893-X","article-title":"Axiom of choice and complementation","volume":"51","author":"Diaconescu R.","year":"1975","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2268484"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2963897"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19780242514"},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","unstructured":"M. E.Maietti About effective quotients in constructive type theory. 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