Parametrizing by the Ellentuck space
Volume 255 / 2021
Fundamenta Mathematicae 255 (2021), 139-157
MSC: Primary 03E05; Secondary 03E99.
DOI: 10.4064/fm86-6-2021
Published online: 7 September 2021
Abstract
A new method is introduced to parametrize topological Ramsey spaces by the Ellentuck space. To demonstrate the strength of these parametrized Ramsey spaces over the Ellentuck space, we give some new proofs of known parametrized perfect set theorems. We generalize our methods by identifying conditions that allow for parametrizations by spaces other then the Ellentuck space. We conclude with some open questions concerning the canonical Ramsey theory of these spaces.
