Ramsey Theory on Generalized Baire Space
Dan Hathaway
TL;DR
This paper explores the applicability of Ramsey theory on generalized Baire space, demonstrating that while some classical theorems fail under the standard topology, analogous results can be established with coarser topologies.
Contribution
It introduces new Ramsey-type theorems for generalized Baire space using alternative topologies, expanding the understanding of combinatorial properties in this setting.
Findings
Galvin-Prikry Theorem does not hold with standard topology
Similar Ramsey theorems hold with coarser topologies
Provides new insights into topological combinatorics on generalized Baire space
Abstract
We show that although the Galvin-Prikry Theorem does not hold on generalized Baire space with the standard topology, there are similar theorems which do hold on generalized Baire space with certain coarser topologies.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical and Theoretical Analysis · Computability, Logic, AI Algorithms