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Proceedings of the American Mathematical Society

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

 
 

 

The consistency strength of certain stationary subsets of $ \mathcal{P}_\kappa \lambda$


Author: Stewart Baldwin
Journal: Proc. Amer. Math. Soc. 92 (1984), 90-92
MSC: Primary 03E55; Secondary 03C55, 03E35, 04A20
DOI: https://doi.org/10.1090/S0002-9939-1984-0749898-9
MathSciNet review: 749898
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Abstract: If $ \kappa \leqslant \lambda $ are uncountable cardinals with $ \kappa $ regular, let $ S\left( {\kappa ,\lambda } \right)$. We investigate the consistency strength of the statement " $ S\left( {\kappa ,\lambda } \right)$ is stationary in $ {\mathcal{P}_\kappa }\lambda $," and prove that it is strictly weaker than "$ \exists $ a Ramsey cardinal," which combines with the lower bound $ \left( {{0^\char93 }} \right)$ proven earlier by J. Baumgartner to give a narrow range of the consistency strength of this statement. In addition, we give an example $ \left( {L\left[ U \right]} \right)$ to show that " $ \exists \lambda > $" does not necessarily imply " $ S\left( {\kappa ,{\kappa ^ + }} \right)$ is stationary."


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DOI: https://doi.org/10.1090/S0002-9939-1984-0749898-9
Article copyright: © Copyright 1984 American Mathematical Society

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