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20242026
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math.LO2026

Strong Topological Rokhlin Property: Finite-Index Ascent, Descriptive Complexity, and Effective Obstructions

Jintao Luo

We give a finite symbolic characterization of the strong topological Rokhlin property in terms of globally realizable finite pattern systems. We use this characterization to prove…

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…

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…

math.LO2024

Maximal eventually different families for uniformly weak Ramsey ideals

Jialiang He, Jintao Luo, David Schrittesser +1

We study -maximal eventually different families of functions from the set of natural numbers into itself where is an arbitrary ideal on the set of natural…