Parametrizing the Ramsey theory of vector spaces I: Discrete spaces
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866911684500652032 |
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| author | Smythe, Iian B. |
| author_facet | Smythe, Iian B. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2108_00544 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Parametrizing the Ramsey theory of vector spaces I: Discrete spaces Smythe, Iian B. Combinatorics Logic 05D10, 03E05 (Primary), 15A03 (Secondary) 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. |
| title | Parametrizing the Ramsey theory of vector spaces I: Discrete spaces |
| topic | Combinatorics Logic 05D10, 03E05 (Primary), 15A03 (Secondary) |
| url | https://arxiv.org/abs/2108.00544 |