3 papers
math.LO2026
Homogeneous hypergraph regularity lemmas via -strong honest definitions
Mervyn Tong
We prove that -uniform hypergraphs definable in an NIP strongly -distal structure satisfy a homogeneous regularity lemma -- they can be partitioned into a bounded number…
math.LO2026
Higher-arity distality and forking triviality
Mervyn Tong
Answering a question of Goode, we show that -triviality collapses to (1-)triviality among simple theories. In particular, every stable theory with quantifier elimination in a re…
math.CO2024
Zarankiewicz bounds from distal regularity lemma
Mervyn Tong
Since Kővári, Sós, and Turán proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting t…