Set theory in infinite-dimensional vector spaces

Smythe, Iian B.

doi:10.7298/x4bk19h2

2017

DOI: 10.7298/x4bk19h2

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Set theory in infinite-dimensional vector spaces

Iian B. Smythe¹

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A local Ramsey theory for block sequences

Smythe

2018

Trans. Amer. Math. Soc.

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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 [N] ∞ . Under large cardinals, these results are extended to partitions in L(R) and L(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. . He would also like to thank his PhD advisor, Justin Tatch Moore, for continued guidance and suggesting the problem of characterizing L(R)-generic filters for the projections in the Calkin algebra which motivated this work.

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A local Ramsey theory for block sequences

Smythe

2018

Trans. Amer. Math. Soc.

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Filters on a countable vector space

Smythe¹

2023

Fund. Math.

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Set theory in infinite-dimensional vector spaces

Cited by 2 publications

References 33 publications

A local Ramsey theory for block sequences

A local Ramsey theory for block sequences

Filters on a countable vector space

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