Henry Towsner

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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…

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…

The finite big Ramsey degrees of Henson graphs are provable in ACA0​

The Complexity of the Set of Validities of a Theory

Hanf Locality and Invariant Elementary Definability

A classification of incompleteness statements

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