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math.LO2026
Computable aspects of the Laver partition theorem
Alberto Marcone, Gian Marco Osso
The Laver Partition Theorem is a fundamental tool in the analysis of Laver and Hechler forcings. It is also connected to determinacy and the Galvin-Prikry theorem: indeed it can be…
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'…