Ramsey subsets of the space of infinite block sequences of vectors

2018/10/23 by Daniel Calderón, Calderon, Daniel, Carlos Di Prisco +3 · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Primary 05E35 #Secondary 03E55

paper · doi:10.48550/arxiv.1810.10054

openalex publication_date 2018/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study families of infinite block sequences of elements of the space \FIN_k. 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 k=1 fit in the theory of the Ramsey space of infinite block sequences of finite sets of natural numbers.

Cited by

• There may be exactly n Q-points

Related

• Parametrizing the Ramsey theory of vector spaces I: Discrete spaces
• Coideals of block sequences
• Local Ramsey theory. An abstract approach
• Topological Ramsey Spaces Dense in Forcings
• Parametrized Ramsey theory of infinite block sequences of vectors