Selective Independence and $h$-Perfect Tree Forcing Notions

Corey Bacal Switzer

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arXiv · 2202.12046

Selective Independence and $h$-Perfect Tree Forcing Notions

Corey Bacal Switzer

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Abstract

Generalizing the proof for Sacks forcing, we show that the $h$-perfect tree forcing notions introduced by Goldstern, Judah and Shelah preserve selective independent families even when iterated. As a result we obtain new proofs of the consistency of $\mathfrak{i} = \mathfrak{u} < \mathrm{non} (\mathcal N) = \mathrm{cof} (\mathcal N)$ and $\mathfrak{i} < \mathfrak{u} = \mathrm{non} (\mathcal N) = \mathrm{cof}( \mathcal N)$ as well as some related results.

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BibTeX RIS

Corey Bacal Switzer. 2022-02-24. Selective Independence and $h$-Perfect Tree Forcing Notions. https://arxiv.org/abs/2202.12046

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