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arXiv · 2601.08718

Strong Projective Witnesses

Vera Fischer·Julia Millhouse
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Abstract

We show Shelah's original creature forcing from 1984 strongly preserves tight mad families. In particular, answering questions of Fischer and Friedman and Friedman and Zdomskyy, we show the constellation $\aleph_1 = \mathfrak{a} < \mathfrak{s} = \aleph_2$ is consistent with the existence of a $\Delta_3^1$ wellorder of the reals and tight mad families of sizes $\aleph_1, \aleph_2$ which are $\Pi_1^1, \Pi_2^1$-definable, respectively. Each of these projective definitions is of minimal possible complexity.

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Vera Fischer, Julia Millhouse. 2026-01-13. Strong Projective Witnesses. https://arxiv.org/abs/2601.08718

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