Partition Forcing and Independent Families

Journal of Symbolic Logic 88 (4):1590-1612 (2023)
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Abstract

We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$. In addition, we show that Shelah’s poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$.

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Citations of this work

Cohen preservation and independence.Vera Fischer & Corey Bacal Switzer - 2023 - Annals of Pure and Applied Logic 174 (8):103291.

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References found in this work

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Iterated perfect-set forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
Mad families, splitting families and large continuum.Jörg Brendle & Vera Fischer - 2011 - Journal of Symbolic Logic 76 (1):198 - 208.
Ideals of independence.Vera Fischer & Diana Carolina Montoya - 2019 - Archive for Mathematical Logic 58 (5-6):767-785.
Matrix iterations and Cichon’s diagram.Diego Alejandro Mejía - 2013 - Archive for Mathematical Logic 52 (3-4):261-278.

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