On the relationship between mutual and tight stationarity

Annals of Pure and Applied Logic:102963 (2021)
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Abstract

We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary subsets consisting of cofinality ω_1 ordinals, and show that such stationary sequences are mutually stationary in the presence of interleaved supercompact cardinals.

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William Chen
Reed College

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References found in this work

Notes on Singular Cardinal Combinatorics.James Cummings - 2005 - Notre Dame Journal of Formal Logic 46 (3):251-282.
Diagonal Prikry extensions.James Cummings & Matthew Foreman - 2010 - Journal of Symbolic Logic 75 (4):1383-1402.
On singular stationarity II.Omer Ben-Neria - 2019 - Journal of Symbolic Logic 84 (1):320-342.

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