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math.LO2026
Van Douwen Families, Productivity and Ultrafilter Maximality
Jialiang He, Jintao Luo, Hang Zhang
We study idealized maximal eventually different families through Van Douwen maximality, productivity, and ultrafilter maximality. We show that Van Douwen -MED families…
math.LO2026
Open Problems in Mathematical Logic
George Barmpalias, Su Gao, Jialiang He +8
These open problems were presented in the Problem Sessions held during the Tianyuan Workshop on Definability and Computation, June 22-26, 2026. The problems are organized into sect…
math.LO2026
Ramsey Property and Pathological Sets: Almost Disjointness, Independence and Other Maximal Objects
Jialiang He, Jintao Luo, Shuguo Zhang
We show that under , if the Ramsey property holds for all sets in a good pointclass , then there is no MAD family in , proving a long-s…