Sebastian Junge | Searcharxiv

arXiv2025

Self-Dual Ramsey Degrees for Trees

We consider a Ramsey statement for pairs of maps between trees, where one is an embedding as defined by Deuber and the other is a rigid surjection as defined by Solecki. We show that there is no Ramsey Theorem for pairs of maps where the coloring depends on both coordinates. On the other hand, we give a characterization of the Ramsey degrees for such pairs. Furthermore, we show that our theorem on Ramsey Degrees for pairs of maps between trees implies the Ramsey Theorem for pairs of maps between linear orders as proved by Solecki.

math.CO↗

arXiv2022

Categorical view of the Partite Lemma in structural Ramsey Theory

We construct of the main object of the Partite Lemma as the colimit over a certain diagram. This gives a purely category theoretic take on the Partite Lemma and establishes the canonicity of the object. Additionally, the categorical point of view allows us to unify the direct Partite Lemma in the Ne\v{s}et\v{r}il--R\"odl Theorem with the dual Paritite Lemma by Solecki.

math.CO↗