A local Ramsey theory for block sequences
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- by Iian B. Smythe PDF
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Abstract:
We develop local forms of Ramsey-theoretic dichotomies for block sequences in infinite-dimensional vector spaces, analogous to Mathias’s 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.References
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Additional Information
- Iian B. Smythe
- Affiliation: Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854
- MR Author ID: 1197541
- ORCID: 0000-0003-2771-5025
- Email: i.smythe@rutgers.edu
- Received by editor(s): September 28, 2016
- Received by editor(s) in revised form: October 20, 2017
- Published electronically: August 15, 2018
- Additional Notes: The author is partially supported by NSERC award PGSD2-453779-2014 and NSF grant DMS-1600635.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 8859-8893
- MSC (2010): Primary 05D10, 03E05; Secondary 46B20
- DOI: https://doi.org/10.1090/tran/7448
- MathSciNet review: 3864398