A weak variation of Shelah's I[ω₂]

Journal of Symbolic Logic 69 (1):94-100 (2004)
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Abstract

We use a $\kappa^{+}-Mahlo$ cardinal to give a forcing construction of a model in which there is no sequence $\langle A_{\beta} : \beta \textless \omega_{2} \rangle$ of sets of cardinality $\omega_{1}$ such that $\{\lambda \textless \omega_{2} : \existsc \subset \lambda & (\bigcupc = \lambda otp(c) = \omega_{1} & \forall \beta \textless \lambda (c \cap \beta \in A_{\beta}))\}$ is stationary

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William Mitchell
University of Alabama, Birmingham

Citations of this work

On the Hamkins approximation property.William J. Mitchell - 2006 - Annals of Pure and Applied Logic 144 (1-3):126-129.
Adding Closed Unbounded Subsets of ω₂ with Finite Forcing.William J. Mitchell - 2005 - Notre Dame Journal of Formal Logic 46 (3):357-371.
An equiconsistency result on partial squares.John Krueger & Ernest Schimmerling - 2011 - Journal of Mathematical Logic 11 (1):29-59.
Guessing models and the approachability ideal.Rahman Mohammadpour & Boban Veličković - 2020 - Journal of Mathematical Logic 21 (2):2150003.
Separating weak partial square principles.John Krueger & Ernest Schimmerling - 2014 - Annals of Pure and Applied Logic 165 (2):609-619.

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References found in this work

Some exact equiconsistency results in set theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
Reflecting stationary sets and successors of singular cardinals.Saharon Shelah - 1991 - Archive for Mathematical Logic 31 (1):25-53.

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