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An exact Ramsey principle for block sequences

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Abstract

We prove an exact, i.e., formulated without Δ-expansions, Ramsey principle for infinite block sequences in vector spaces over countable fields, where the two sides of the dichotomic principle are represented by respectively winning strategies in Gowers’ block sequence game and winning strategies in the infinite asymptotic game. This allows us to recover Gowers’ dichotomy theorem for block sequences in normed vector spaces by a simple application of the basic determinacy theorem for infinite asymptotic games. The author was partially supported by NSF grant DMS 0556368.

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Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249) 851 S. Morgan Street, 606077045, Chicago, IL

    Christian Rosendal

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  1. Christian Rosendal
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Correspondence to Christian Rosendal.

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Rosendal, C. An exact Ramsey principle for block sequences. Collect. Math. 61, 25–36 (2010). https://doi.org/10.1007/BF03191223

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  • DOI: https://doi.org/10.1007/BF03191223

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