Determinacy of adversarial Gowers games
Volume 227 / 2014
Fundamenta Mathematicae 227 (2014), 163-178
MSC: Primary 46B03; Secondary 03E15.
DOI: 10.4064/fm227-2-3
Abstract
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.
