GENERIC ULTRAFILTERS AND TRANSITIVE MODELS OF ZFC
John Bell · Oxford University Press eBooks · 2005
The construction of V(B) is relativized to transitive models of ZFC and shown to give rise to actual models of ZFC, in which various set-theoretic assertions are falsified. Boolean-valued set theory is thereby transformed into a valuable model-theoretic tool. The notion of a generic ultrafilter in a Boolean-valued model is introduced in this chapter and shown to play a key role in the discussion.