# Parametrizing the Ramsey theory of block sequences I: Discrete vector spaces

@inproceedings{Smythe2021ParametrizingTR, title={Parametrizing the Ramsey theory of block sequences I: Discrete vector spaces}, author={Iian B. Smythe}, year={2021} }

We show that the Ramsey theory of block sequences in infinite-dimensional vector spaces can be parametrized by perfect sets. This is applied to prove combinatorial dichotomies concerning families of linear transformations and partitions of vector spaces, respectively. We also prove a (necessarily partial) preservation result for analogues of selective ultrafilters in this setting, under Sacks forcing.

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Filters on a countable vector space

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We study various combinatorial properties, and the implications between them, for filters generated by infinite-dimensional subspaces of a countable vector space. These properties are analogous to… Expand

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