Meager Sets, Games and Singular Cardinals

TL;DR

This paper establishes an equivalence between a topological game theory statement about winning strategies with limited memory and a weak form of the Singular Cardinals Hypothesis, linking game theory with set-theoretic cardinal properties.

Contribution

It introduces a novel equivalence connecting game-theoretic strategies to a fundamental hypothesis in set theory, expanding understanding of their interplay.

Findings

Equivalence between game strategies and the Singular Cardinals Hypothesis.

Limited memory strategies correspond to a weak form of the hypothesis.

Bridges between topological game theory and set theory are demonstrated.

Abstract

We show that a statement concerning the existence of winning strategies of limited memory in an infinite two-person topological game is equivalent to a weak version of the Singular Cardinals Hypothesis.