Corpus ID: 236772719

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. 
1 Citations
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