## Some stationary subsets of $\mathcal {P}(\lambda )$

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- by Hans-Dieter Donder, Peter Koepke and Jean-Pierre Levinski
- Proc. Amer. Math. Soc.
**102**(1988), 1000-1004 - DOI: https://doi.org/10.1090/S0002-9939-1988-0934882-6
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## Abstract:

Let $\kappa$ and $\lambda$ be*uncountable cardinals*such that $\kappa \leq \lambda$, and set $S(\kappa ,\lambda ) = \left \{ {X \in {\mathcal {P}_\kappa }(\lambda )|\;|X \cap \kappa | < |X|} \right \}$. We determine the consistency strength of the statement "$\left ( {\exists \lambda \geq \kappa } \right )$($(S(\kappa ,\lambda )$ is stationary in ${\mathcal {P}_\kappa }(\lambda )$)" using a new type of partition cardinals. In addition, we show that the property "$S(\kappa ,{\kappa ^ + })$ is stationary in ${\mathcal {P}_\kappa }({\kappa ^ + })$" is much stronger.

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## Bibliographic Information

- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**102**(1988), 1000-1004 - MSC: Primary 03E55; Secondary 03E05, 03E35
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934882-6
- MathSciNet review: 934882