Shuguo Zhang

collaborators

2 papers

math.LO2026

Ramsey Property and Pathological Sets: Almost Disjointness, Independence and Other Maximal Objects

Jialiang He, Jintao Luo, Shuguo Zhang

We show that under $ZF + CC_{R}$ , if the Ramsey property holds for all sets in a good pointclass $I^$ , then there is no MAD family in $I^$ , proving a long…

math.LO2025

Ramsey regularity implies no MAD families without uniformization

Jialiang He, Jintao Luo, Shuguo Zhang

We show that if the Ramsey property holds (in a class of sets), then there is no MAD family (in this class, provided it satisfies some modest closure properties), proving a conject…