Ramsey subsets of the space of infinite block sequences of vectors
Volume 257 / 2022
Fundamenta Mathematicae 257 (2022), 189-216
MSC: Primary 05C55, 05D10; Secondary 03E05.
DOI: 10.4064/fm129-10-2021
Published online: 7 February 2022
Abstract
We study families of infinite block sequences of elements of the space $\mathrm {FIN}_k$. In particular we study Ramsey properties of such families and Ramsey properties localized on 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 $k=1$, fit in the theory of the Ramsey space of infinite block sequences of finite sets of natural numbers.
