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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
DOI: https://doi.org/10.1090/S0002-9939-1988-0934882-6
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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  • [1] S. Baldwin, Generalizing the Mahlo hierarchy, with applications to the Mitchell models, Ann. Pure Appl. Logic 25 (1983), 103-127. MR 725730 (85d:03106)
  • [2] -, The consistency strength of certain stationary subsets of $ {\mathcal{P}_\kappa }(\lambda )$, Proc. Amer. Math. Soc. 92 (1984), 90-92.
  • [3] C. A. Di Prisco and W. Marek, A filter on $ {[\lambda ]^\kappa }$, Proc. Amer. Math. Soc. 90 (1984), 591-598. MR 733412 (85g:03072)
  • [4] A. J. Dodd, The core model, London Math. Soc. Lecture Notes, no. 61, Cambridge Univ. Press, 1982. MR 652253 (84a:03062)
  • [5] H.-D. Donder, R. B. Jensen and B. Koppelberg, Some applications of $ K$, Set Theory and Model Theory (Proc. Bonn 1979), Lecture Notes in Math., vol. 872, Springer-Verlag, Berlin and New York, 1981, pp. 55-97. MR 645907 (83c:03032)
  • [6] H.-D. Donder and P. Koepke, On the consistency strength of "accessible" Jonsson cardinals and of the weak Chang conjecture, Ann. Pure Appl. Logic 25 (1983), 233-261. MR 730856 (85j:03084)
  • [7] J.-P. Levinski, Instances of the conjecture of Chang, Israel J. Math. 48 (1984), 225-243. MR 770703 (86k:03047)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934882-6
Keywords: Partition cardinals, core model, stationary
Article copyright: © Copyright 1988 American Mathematical Society

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