Abstract.
A question of Foreman and Magidor asks if it is consistent for every sequence of stationary subsets of the ℵ n ’s for 1≤n<ω to be mutually stationary. We get a positive answer to this question in the context of the negation of the Axiom of Choice. We also indicate how a positive answer to a generalized version of this question in a choiceless context may be obtained.
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The author wishes to thank James Cummings for helpful correspondence on the subject matter of this paper. The author also wishes to thank the referee and Andreas Blass, the corresponding editor, for helpful comments and suggestions that have been incorporated into this version of the paper. 03E35, 03E55 Supercompact cardinal – Indestructibility – Almost huge cardinal – Mutual stationarity – Symmetric inner model
Revised version: 6 June 2004
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Apter, A. On a problem of Foreman and Magidor. Arch. Math. Logic 44, 493–498 (2005). https://doi.org/10.1007/s00153-004-0259-6
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DOI: https://doi.org/10.1007/s00153-004-0259-6