GENERIC ULTRAFILTERS AND TRANSITIVE MODELS OF ZFC
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.
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