Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. II

TL;DR

This paper explores the connections between model-theoretical properties, ultrafilter uniformity, and topological compactness, providing multiple equivalent conditions and deepening understanding of their interrelations.

Contribution

It introduces new equivalent conditions for a model-theoretical property involving ultrafilters and topological compactness, expanding theoretical frameworks.

Findings

Multiple conditions equivalent to the property $$

Connections established between ultrafilter uniformity and topological compactness

Existence of certain infinite matrices related to the property

Abstract

We find many conditions equivalent to the model-theoretical property $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in [L1]. Our conditions involve uniformity of ultrafilters, compactness properties of products of topological spaces and the existence of certain infinite matrices.