Henry Towsner

collaborators

6 papers

math.LO2026

The finite big Ramsey degrees of Henson graphs are provable in $ACA_{0}$

Peter Cholak, Natasha Dobrinen, Henry Towsner

Let $H_{n + 1}$ denote a computable copy of the $(n + 1)$ -clique free universal homogeneous Henson graph, $G$ denote a finite subgraph of $H_{n + 1}$ , and $k (G, n)$ deno…

math.LO2026

The Complexity of the Set of Validities of a Theory

Denis R. Hirschfeldt, Henry Towsner, Scott Weinstein

We study the collection of first-order logical schemata all of whose instances are theorems of a given theory $T$ ; we call these the validities of $T$ ( $V (T)$ ). It is easy…

stat.ML2025

Higher-arity PAC learning, VC dimension and packing lemma

Artem Chernikov, Henry Towsner

The aim of this note is to overview some of our work in Chernikov, Towsner'20 (arXiv:2010.00726) developing higher arity VC theory (VC $_{n}$ dimension), including a generalization of…

math.CO2025

Averages of hypergraphs and higher arity stability

Artem Chernikov, Henry Towsner

We show that $k$ -ary functions giving the measure of the intersection of multi-parametric families of sets in probability spaces, e.g. $(x,y,z) \in X \times Y \times Z \mapsto Î¼(P…

math.LO2025

Hanf Locality and Invariant Elementary Definability

Steven Lindell, Henry Towsner, Scott Weinstein

We introduce some notions of invariant elementary definability which extend the notions of first-order order-invariant definability, and, more generally, definability invariant wit…

math.LO2025

A classification of incompleteness statements

Henry Towsner, James Walsh

For which choices of $X, Y, Z \in {I^£_{1}^{1}, I^_{1}^{1}}$ does no sufficiently strong $X$ -sound and $Y$ -definable extension theory prove its own $Z$ -soundness? We give a complete answer, th…