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.
Σ1 2 and Π1 1 mad families.The Journal of Symbolic Logic, 78(4):1181–1182
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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.