### RVM, RVC revisited: Clubs and Lusin sets

by Kumar and Shelah. [KmSh:1046]

A cardinal kappa is Cohen measurable (RVC) if for some
kappa-additive ideal {I} over kappa, {P}(kappa)
slash {I} is forcing isomorphic to adding lambda
Cohen reals for some lambda . Such cardinals can be obtained
by starting with a measurable cardinal kappa and adding at
least kappa Cohen reals. We construct various models of RVC
with different properties than this model.Our main results are:
(1) kappa = 2^{omega} is RVC does not decide
club_S for various stationary S subseteq kappa .
(2) kappa <= lambda = cf(lambda) < 2^{omega} does
not decide club_S for various stationary S subseteq lambda .
(3) kappa = 2^{omega} is RVC does not decide the existence
of a Lusin set of size kappa .

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