Ramsey subsets of the space of infinite block sequences of vectors
Daniel Calderon, Carlos Di Prisco, Jose G. Mijares
TL;DR
This paper investigates Ramsey properties of infinite block sequences in the space of finite sets, connecting ultrafilters and coideals to Ramsey theory in this context.
Contribution
It extends the theory of Ramsey spaces by analyzing how ultrafilters and coideals relate to Ramsey properties of infinite block sequences.
Findings
Stable ordered-union ultrafilters fit into the Ramsey space framework.
Matet-adequate families are connected to Ramsey properties for k=1.
Localization of Ramsey properties to selective coideals is established.
Abstract
We study families of infinite block sequences of elements of the space . In particular we study Ramsey properties of such families and Ramsey properties localized to a selective or semiselective coideal. We show how the stable ordered-union ultrafilters defined by Blass, and Matet-adequate families defined by Eisworth in the case fit in the theory of the Ramsey space of infinite block sequences of finite sets of natural numbers.
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