1 citations · 1 across the 5 of their papers we have counts for
5 papers
Combinatorics in 1-semi-equational theories
Mervyn Tong
We give direct combinatorial proofs that 1-semi-equational theories satisfy two combinatorial properties that imply the non-interpretability of certain fields. Our main result is t…
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…
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…
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…
Distal expansions of Presburger arithmetic by a sparse predicate
Mervyn Tong
We prove that the structure is distal for all congruence-periodic sparse predicates . We do so by constructing strong honest definitions…