Gian Marco Osso

collaborators

4 papers

math.LO2026

Listing the hyperarithmetical functions

Joseph S. Miller, Gian Marco Osso, Isabella Scott

Given a countable Turing ideal $I \subseteq I ¨ ^{I ¨} $ , we say that $x$ is a list (resp. weak list) of $I$ if $I = {x^{[n]} : n \in I ¨ }$ (resp. if $\mathc…

math.LO2026

Forcing and classes of $HYP$ -dominating functions

Noam Greenberg, Gian Marco Osso

We study the question, what computational power is sufficient to perform constructions using either Laver or Hechler forcing. As a result, we obtain a separation between three rela…

math.LO2026

The reverse mathematics of Brooks' theorem

Alberto Marcone, Gian Marco Osso

This is an analysis of the status of Brooks' Theorem, a celebrated result in graph coloring, from the point of view of Reverse Mathematics. We prove that the restriction of Brooks'…

math.LO2024

The Galvin-Prikry Theorem in the Weihrauch lattice

Alberto Marcone, Gian Marco Osso

This paper classifies different fragments of the Galvin-Prikry theorem, an infinite dimensional generalization of Ramsey's theorem, in terms of their uniform computational content…

Listing the hyperarithmetical functions

Forcing and classes of HYP-dominating functions

The reverse mathematics of Brooks' theorem

The Galvin-Prikry Theorem in the Weihrauch lattice

Forcing and classes of $HYP$ -dominating functions