Filter games and combinatorial properties of winning strategies
Claude Laflamme
TL;DR
This paper characterizes winning strategies in infinite filter-based games through combinatorial and structural properties, generalizing previous ultrafilter game results.
Contribution
It introduces a unifying framework for understanding winning strategies in infinite games involving filters, extending prior ultrafilter game analyses.
Findings
Characterization of winning strategies via combinatorics and structure
Generalization of ultrafilter games of Galvin
New insights into infinite filter-based games
Abstract
We characterize winning strategies in various infinite games involving filters on the natural numbers in terms of combinatorics or structural properties of the given filter. These generalize several ultrafilter games of Galvin.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Computability, Logic, AI Algorithms