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.
Combinatorial cardinal characteristics of the continuum
2 Pith papers cite this work. Polarity classification is still indexing.
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Separations are obtained between three relativised non-lowness classes as computability analogues of cardinals in Cichon's diagram via Laver and Hechler forcing.
citing papers explorer
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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.
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Forcing and classes of $\mathsf{HYP}$-dominating functions
Separations are obtained between three relativised non-lowness classes as computability analogues of cardinals in Cichon's diagram via Laver and Hechler forcing.