This is an announcement for the paper "An exact Ramsey principle for block sequences" by Christian Rosendal.
Abstract: We prove an exact, i.e., formulated without $\Delta$-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.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 46B03, 03E15
The source file(s), ExactRamseyPrinciples17submitted.tex: 37130 bytes, is(are) stored in gzipped form as 0807.2205.gz with size 11kb. The corresponding postcript file has gzipped size 82kb.
Submitted from: rosendal@math.uiuc.edu
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http://front.math.ucdavis.edu/0807.2205
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http://arXiv.org/abs/0807.2205
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