# Sh:1046

• Kumar, A., & Shelah, S. RVM, RVC revisited: Clubs and Lusin sets. Preprint.
• Abstract:
A cardinal \kappa is Cohen measurable (RVC) if for some \kappa-additive ideal \mathcal{I} over \kappa, \mathcal{P}(\kappa) / \mathcal{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 \clubsuit_S for various stationary S \subseteq \kappa. (2) \kappa \leq \lambda = cf(\lambda) < 2^{\omega} does not decide \clubsuit_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.
@article{Sh:1046,
}