Abstract
We show that the existence of a \({\Pi^1_1}\)-definable mad family is consistent with the existence of a \({\Delta^{1}_{3}}\)-definable well-order of the reals and \({\mathfrak{b}=\mathfrak{c}=\aleph_3}\).
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Fischer, V., Friedman, S.D. & Khomskii, Y. Co-analytic mad families and definable wellorders. Arch. Math. Logic 52, 809–822 (2013). https://doi.org/10.1007/s00153-013-0345-8
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DOI: https://doi.org/10.1007/s00153-013-0345-8