Peter Cholak

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math.LO2026

Ramsey Theory and Bounding in Arithmetic

Peter Cholak

We explore the relation between various versions of Ramsey theorem and bounding schemes in model $N$ of a fragment of arithmetic $F$ . Our goal is to recast, in a different framew…

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 Henson graphs: colorings and codings

Peter Cholak, Natasha Dobrinen, Charlie McCoy

By recent work of \citet{DobrinenICM} and \citet{Balko7} we know that every finite $G$ in the Henson graph $H_{n + 1}$ (the universal ultrahomogeneous $(n + 1)$ -clique free gr…

math.LO2025

Low $_{2}$ computably enumerable sets have hyperhypersimple supersets

Peter Cholak, Rodney Downey, Noam Greenberg

A longstanding question is to characterize the lattice of supersets (modulo finite sets), $L^{*} (A)$ , of a low $_{2}$ computably enumerable (c.e.) set. The conjecture is that…

Ramsey Theory and Bounding in Arithmetic

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

The Henson graphs: colorings and codings

Low2​ computably enumerable sets have hyperhypersimple supersets

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

Low $_{2}$ computably enumerable sets have hyperhypersimple supersets