Determinacy of adversarial Gowers games

Volume 227 / 2014

Christian Rosendal Fundamenta Mathematicae 227 (2014), 163-178 MSC: Primary 46B03; Secondary 03E15. DOI: 10.4064/fm227-2-3


We prove a game-theoretic dichotomy for $G_{\delta \sigma }$ sets of block sequences in vector spaces that extends, on the one hand, the block Ramsey theorem of W. T. Gowers proved for analytic sets of block sequences and, on the other hand, M. Davis' proof of ${\bf \Sigma }^0_3$ determinacy.


  • Christian RosendalDepartment of Mathematics, Statistics and Computer Science (M/C 249)
    University of Illinois at Chicago
    851 S. Morgan St.
    Chicago, IL 60607-7045, U.S.A.

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