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The cumulative hierarchy and the constructible universe of ZFA
Author(s) -
Viale Matteo
Publication year - 2004
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310080
Subject(s) - mathematics , operator (biology) , hierarchy , closure (psychology) , universe , connection (principal bundle) , point (geometry) , pure mathematics , combinatorics , geometry , physics , astrophysics , biochemistry , chemistry , repressor , transcription factor , economics , market economy , gene
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 Gödel operation in addition to the standard ones in order to obtain the “constructible” model of ZFA as the least fixed point of the continuous operator of Gödel closure with respect to the standard and the new Gödel operations. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)