On preimages of ultrafilters in ZF
Horst Herrlich, Paul Howard, Kyriakos Keremedis (2016)
Commentationes Mathematicae Universitatis Carolinae
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We show that given infinite sets and a function which is onto and -to-one for some , the preimage of any ultrafilter of under extends to an ultrafilter. We prove that the latter result is, in some sense, the best possible by constructing a permutation model with a set of atoms and a finite-to-one onto function such that for each free ultrafilter of its preimage under does not extend to an ultrafilter. In addition, we show that in there exists an ultrafilter compact...