Under ZF + CC_R, Ramsey property on a pointclass Γ implies no MAD families (or I-MAD for analytic ideals) in Γ, proving Mathias' conjecture, with parallel results for independent families and Vitali sets.
Mad families constructed from perfect almost disjoint families.The Journal of Symbolic Logic, 78(4):1164–1180
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Ramsey Property and Pathological Sets: Almost Disjointness, Independence and Other Maximal Objects
Under ZF + CC_R, Ramsey property on a pointclass Γ implies no MAD families (or I-MAD for analytic ideals) in Γ, proving Mathias' conjecture, with parallel results for independent families and Vitali sets.