Peter Cholak

collaborators

6 papers

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…

cs.CC2026

Algorithmic Information Bounds for Distances and Orthogonal Projections

Peter Cholak, Marianna CsÃ¶rnyei, Neil Lutz +3

We introduce a new technique for proving bounds on the Kolmogorov complexity of geometric objects in Euclidean space, such as points and lines. We apply this technique to prove two…

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…

math.CA2025

Bounding the dimension of exceptional sets for orthogonal projections

Peter Cholak, Marianna Csornyei, Neil Lutz +3

It is well known that if $A \subseteq R^{n}$ is an analytic set of Hausdorff dimension $a$ , then $dim_{H} (I ¨ _{V} A) = min {a, k}$ for a.e.\ $V \in G (n, k)$ , where $G (n, k)$ denotes…

Ramsey Theory and Bounding in Arithmetic

Algorithmic Information Bounds for Distances and Orthogonal Projections

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

Bounding the dimension of exceptional sets for orthogonal projections

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

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