NNR Revisited

by Shelah. [Sh:656]

We are interested in proving that if we use CS iterations of forcing notions not adding reals and additional conditions then the limit forcing does not add reals. As a result we prove that we can amalgamate two earlier methods and so can prove the consistency with ZFC + G.C.H. of two statements gotten separately earlier: SH and non-club guessing. We also prove the consistency of further cases of ``non-club guessing''.

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