Analytic and coanalytic families of almost disjoint functions

Journal of Symbolic Logic 73 (4):1158-1172 (2008)
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Abstract

If F ⊆ NN is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable H ⊆ NN. no member of which is covered by finitely many functions from F, there is f ∈ F such that for all h ∈ H there are infinitely many integers k such that f(k) = h(k). However if V = L then there exists a coanalytic family of pairwise eventually different functions satisfying this strong maximality condition

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Yi Zhang
Humboldt-University, Berlin

Citations of this work

Projective Mad Families.Sy-David Friedman & Lyubomyr Zdomskyy - 2010 - Annals of Pure and Applied Logic 161 (12):1581-1587.
Co-Analytic Mad Families and Definable Wellorders.Vera Fischer, Sy David Friedman & Yurii Khomskii - 2013 - Archive for Mathematical Logic 52 (7-8):809-822.
Isomorphism Types of Maximal Cofinitary Groups.Bart Kastermans - 2009 - Bulletin of Symbolic Logic 15 (3):300-319.
A Co-Analytic Maximal Set of Orthogonal Measures.Vera Fischer & Asger Törnquist - 2010 - Journal of Symbolic Logic 75 (4):1403-1414.

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References found in this work

Happy Families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Infinite Combinatorics and Definability.Arnold W. Miller - 1989 - Annals of Pure and Applied Logic 41 (2):179-203.
Analytic Ideals and Their Applications.Sławomir Solecki - 1999 - Annals of Pure and Applied Logic 99 (1-3):51-72.
Splittings.A. Kamburelis & B. W’Glorz - 1996 - Archive for Mathematical Logic 35 (4):263-277.

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