The cumulative hierarchy and the constructible universe of ZFA

摘要

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?del 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 G?del closure with respect to the standard and the new G?del operations.