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Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory

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Class Forcing and Genericity: Predense sets vs Dense classes

In short my question is: why do we use definable classes in the definition of genericity for class forcing, instead of predense sets. … I'm actually most interested in the situation of Prikry forcing over a model with an $M$-ultrafilter. [1] Stanley, M.C., 2003, Outer Models and Genericity. JSL. …
Chris Le Sueur's user avatar