Year: 2026
Type: preprint
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 $Δ_3^1$ wellorder of the reals and tight mad families of sizes $\aleph_1, \aleph_2$ which are $Π_1^1, Π_2^1$-definable, respectively. Each of these projective definitions is of minimal possible complexity.
Source: arXiv (Cornell University)
Authors: Fischer, Vera, Millhouse, Julia
Institution: University of Vienna
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7124141241
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