Parametrizing the Ramsey theory of vector spaces I: Discrete spaces

Annals of Pure and Applied Logic 2026 Open access

Read full text
Authors: Iian B. Smythe
DOI: 10.1016/j.apal.2026.103791
Cited by: 0
References: 40

Abstract

We show that the Ramsey theory of block sequences in infinite-dimensional discrete vector spaces can be parametrized by perfect sets. As special cases, we prove combinatorial dichotomies for definable families of partitions and linear transformations on those spaces. We also consider the extent to which analogues of selective ultrafilters in this setting are preserved by Sacks forcing.

Fields of Study & Subjects

Advanced Topology and Set Theory Advanced Banach Space Theory Mathematical Dynamics and Fractals

Publication details

Journal / source
Annals of Pure and Applied Logic
Publisher
Elsevier BV
Volume
177
Issue
10
Pages
103791–103791
Publication date
14 May 2026
Language
EN