Partition relations for Hurewicz-type selection hypotheses

TL;DR

This paper introduces a general method to simplify Hurewicz-type selection hypotheses into standard forms, enabling new and existing results, and provides Ramsey theoretic characterizations for these hypotheses.

Contribution

It presents a novel reduction technique for Hurewicz-type hypotheses and derives Ramsey theoretic characterizations, expanding the understanding of these selection principles.

Findings

Unified framework for Hurewicz-type hypotheses

New results derived from the reduction method

Ramsey theoretic characterizations established

Abstract

We give a general method to reduce Hurewicz-type selection hypotheses into standard ones. The method covers the known results of this kind and gives some new ones. Building on that, we show how to derive Ramsey theoretic characterizations for these selection hypotheses.