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Ramsey subsets of the space of infinite block sequences of vectors

Volume 257 / 2022

Daniel Calderón, Carlos Augusto Di Prisco, José G. Mijares 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.

Authors

  • Daniel CalderónUniversity of Toronto
    40 St. George Street
    Toronto, Ontario, Canada M5S 2E4
    e-mail
  • Carlos Augusto Di PriscoUniversidad de Los Andes, Cra. 1, 18a–12
    Bogotá, Colombia
    and
    Instituto Venezolano
    de Investigaciones Científicas
    Caracas, Venezuela
    e-mail
  • José G. MijaresCalifornia State University Los Angeles
    5151 State University Drive
    Los Angeles, CA 90032, USA
    e-mail

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