Mervyn Tong

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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.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

Distal expansions of Presburger arithmetic by a sparse predicate

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