A local Ramsey theory for block sequences
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866913435667660800 |
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| author | Smythe, Iian B. |
| author_facet | Smythe, Iian B. |
| contents | We develop local forms of Ramsey-theoretic dichotomies for block sequences in infinite-dimensional vector spaces, analogous to Mathias' selective coideal form of Silver's theorem for analytic partitions of $[\mathbb{N}]^\infty$. Under large cardinals, these results are extended to partitions in $\mathbf{L}(\mathbb{R})$ and $\mathbf{L}(\mathbb{R})$-generic filters of block sequences are characterized. Variants of these results are also established for block sequences in Banach spaces and for projections in the Calkin algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1609_09016 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A local Ramsey theory for block sequences Smythe, Iian B. Logic 05D10, 03E05 (Primary), 46B20 (Secondary) We develop local forms of Ramsey-theoretic dichotomies for block sequences in infinite-dimensional vector spaces, analogous to Mathias' selective coideal form of Silver's theorem for analytic partitions of $[\mathbb{N}]^\infty$. Under large cardinals, these results are extended to partitions in $\mathbf{L}(\mathbb{R})$ and $\mathbf{L}(\mathbb{R})$-generic filters of block sequences are characterized. Variants of these results are also established for block sequences in Banach spaces and for projections in the Calkin algebra. |
| title | A local Ramsey theory for block sequences |
| topic | Logic 05D10, 03E05 (Primary), 46B20 (Secondary) |
| url | https://arxiv.org/abs/1609.09016 |