Mervyn Tong

collaborators

4 papers

math.LO2026

Homogeneous hypergraph regularity lemmas via $k$ -strong honest definitions

Mervyn Tong

We prove that $(k + 1)$ -uniform hypergraphs definable in an NIP strongly $k$ -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 $k$ -triviality collapses to (1-)triviality among simple theories. In particular, every stable theory with quantifier elimination in a re…

math.CO2026

Zarankiewicz bounds from distal regularity lemma

Mervyn Tong

Since KÅvÃ¡ri, SÃ³s, and TurÃ¡n proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricti…

math.LO2024

Distal expansions of Presburger arithmetic by a sparse predicate

Mervyn Tong

We prove that the structure $(Z, <, +, R)$ is distal for all congruence-periodic sparse predicates $R \subseteq N$ . We do so by constructing strong honest definitions…

Homogeneous hypergraph regularity lemmas via k-strong honest definitions

Higher-arity distality and forking triviality

Zarankiewicz bounds from distal regularity lemma

Distal expansions of Presburger arithmetic by a sparse predicate

Homogeneous hypergraph regularity lemmas via $k$ -strong honest definitions