Ahmed Mimouni

collaborators

2 papers

math.LO2026

Ramsey-like theorems and immunities

Ahmed Mimouni, Ludovic Patey

A Ramsey-like theorem is a statement of the form ``For every 2-coloring of $[N]^{2}$ , there exists an infinite set~ $H \subseteq N$ such that $[H]^{2}$ avoids some pat…

math.LO2024

The reverse mathematics of the pigeonhole hierarchy

The infinite pigeonhole principle for $k$ colors ( $RT_{k}^{1}$ ) states, for every $k$ -partition $A_{0} ⊔ \dots ⊔ A_{k - 1} = N$ , the existence of an infinite su…