L. Carlucci

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math.LO2025

Weihrauch reducibility between Ramsey-type theorems and well-ordering principles at the level of $Σ_{2}^{0}$ -induction: A pilot study

Lorenzo Carlucci, Giordano Celli

We study the relations under Weihrauch reducibility of the well-ordering preservation principle for the operator $X \mapsto X^{ω}$ and the Ordered Ramsey Theorem. Both principles are…

math.LO2024★ 1 cited

Ramsey-like theorems for the Schreier barrier

Lorenzo Carlucci, Oriola Gjetaj, Quentin Le Houérou +1

The family of finite subsets $s$ of the natural numbers such that $∣ s ∣ = 1 + min s$ is known as the Schreier barrier in combinatorics and Banach Space theory, and as the family of exa…

math.LO2024

Reductions of well-ordering principles to combinatorial theorems

Lorenzo Carlucci, Leonardo Mainardi, Konrad Zdanowski

A well-ordering principle is a principle of the form: If $X$ is well-ordered then $F (X)$ is well-ordered, where $F$ is some natural operator transforming linear orders into linear…

Weihrauch reducibility between Ramsey-type theorems and well-ordering principles at the level of Σ20​-induction: A pilot study

Ramsey-like theorems for the Schreier barrier

Reductions of well-ordering principles to combinatorial theorems

Weihrauch reducibility between Ramsey-type theorems and well-ordering principles at the level of $Σ_{2}^{0}$ -induction: A pilot study