{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,13]],"date-time":"2023-10-13T05:46:21Z","timestamp":1697175981086},"reference-count":5,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2003,11,26]],"date-time":"2003-11-26T00:00:00Z","timestamp":1069804800000},"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":[[2004,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present two results which shed some more light on the deep connection between ZFA and the standard ZF set theory: First of all we refine a result of Forti and Honsell (see [5]) in order to prove that the universe of ZFA can also be obtained (without appealing to choice) as the least fixed point of a continuous operator and not only as the greatest fixed point of the powerset operator. Next we show that it is possible to define a new absolute G\u00f6del operation in addition to the standard ones in order to obtain the \u201cconstructible\u201d model of ZFA as the least fixed point of the continuous operator of G\u00f6del closure with respect to the standard and the new G\u00f6del operations. (\u00a9 2003 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310080","type":"journal-article","created":{"date-parts":[[2004,1,16]],"date-time":"2004-01-16T15:51:49Z","timestamp":1074268309000},"page":"99-103","source":"Crossref","is-referenced-by-count":3,"title":["The cumulative hierarchy and the constructible universe of ZFA"],"prefix":"10.1002","volume":"50","author":[{"given":"Matteo","family":"Viale","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2003,11,26]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"P.Aczel Non well founded set theories. CSLI Lecture Notes14(CSLI Publications Stanford 1988)."},{"key":"e_1_2_1_3_2","unstructured":"J.Barwise andL.Moss Vicious Circles (CSLI Publications Stanford 1996)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"T.Jech Set Theory (Springer New York 1997).","DOI":"10.1007\/978-3-662-22400-7"},{"key":"e_1_2_1_5_2","first-page":"493","article-title":"Set Theory with free construction principles","volume":"10","author":"Forti M.","year":"1983","journal-title":"Annali Scuola Normale Superiore di Pisa, Cl. Sci."},{"key":"e_1_2_1_6_2","first-page":"69","article-title":"Axioms of choice and free construction principles 1","volume":"36","author":"Forti M.","year":"1984","journal-title":"Bull. Soc. Math. Belg."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310080","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310080","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T08:59:32Z","timestamp":1697101172000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310080"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,11,26]]},"references-count":5,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1002\/malq.200310080"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310080","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,11,26]]}}}