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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Authors: Hans-Dieter Donder, Peter Koepke and Jean-Pierre Levinski
Journal: Proc. Amer. Math. Soc. 102 (1988), 1000-1004
MSC: Primary 03E55; Secondary 03E05, 03E35
MathSciNet review: 934882
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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 )\vert\;\vert X \cap \kappa \vert < \vert X\vert} \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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DOI: https://doi.org/10.1090/S0002-9939-1988-0934882-6
Keywords: Partition cardinals, core model, stationary
Article copyright: © Copyright 1988 American Mathematical Society