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  1. Coanalytic ultrafilter bases.Jonathan Schilhan - 2022 - Archive for Mathematical Logic 61 (3-4):567-581.
    We study the definability of ultrafilter bases on \ in the sense of descriptive set theory. As a main result we show that there is no coanalytic base for a Ramsey ultrafilter, while in L we can construct \ P-point and Q-point bases. We also show that the existence of a \ ultrafilter is equivalent to that of a \ ultrafilter base, for \. Moreover we introduce a Borel version of the classical ultrafilter number and make some observations.
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  • Co-analytic mad families and definable wellorders.Vera Fischer, Sy David Friedman & Yurii Khomskii - 2013 - Archive for Mathematical Logic 52 (7-8):809-822.
    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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  • Bounding, splitting, and almost disjointness.Jörg Brendle & Dilip Raghavan - 2014 - Annals of Pure and Applied Logic 165 (2):631-651.
    We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, the splitting number, and the existence of certain kinds of splitting families.
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