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.
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@article{Sh:1046,
 author = {Kumar, Ashutosh and Shelah, Saharon},
 title = {{RVM, RVC revisited: Clubs and Lusin sets}}
}