4 papers
The barrier Ramsey theorem
Alberto Marcone, Antonio Montalbán, Andrea Volpi
In this paper we study a very general finite Ramsey theorem, where both the sets being colored and the homogeneous set must satisfy some largeness notion. For the homogeneous set t…
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'…
On the learning power of Friedman-Stanley jumps
Vittorio Cipriani, Alberto Marcone, Luca San Mauro
Recently, a surprising connection between algorithmic learning of algebraic structures and descriptive set theory has emerged. Following this line of research, we define the learni…
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…