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PARTITION FORCING AND INDEPENDENT FAMILIES
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 88 / Issue 4 / December 2023
- Published online by Cambridge University Press:
- 03 October 2022, pp. 1590-1612
- Print publication:
- December 2023
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- Article
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- You have access
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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 
$\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$.
