Peter Cholak

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20242026

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math.LO2024

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.CA2024

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 $dim_{H} (π_{V} A) = min {a, k}$ for a.e.\ $V \in G (n, k)$ , where $G (n, k)$ denotes t…

Low2​ computably enumerable sets have hyperhypersimple supersets

Bounding the dimension of exceptional sets for orthogonal projections

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