Tuesday, January 8, 2019, 15.00
Howard House 4th Floor Seminar Room, University of Bristol
Speaker: Arno Pauly (Swansea University)
Title: Uniformity aspects of determinacy
We consider uniformity aspects of determinacy for some low-level point-classes. The formal framework for this is Weihrauch reducibility, which will be introduced. We distinguish two cases: For games on Cantor space with winning sets from the Hausdorff difference hierarchy, we find that there is a player such that the knowledge that she will win does not help the task of a constructing a winning strategy. This does not hold for open winning sets on Baire space — here knowing who wins the game makes it easier to construct a winning strategy. Open determinacy on Baire space shares all known properties with the perfect tree theorem (a closed subset of Baire space is either countable or contains a perfect subset), but it is an open question whether they are actually equivalent.
The results presented are from joint work with Takayuki Kihara and Alberto Marcone (https://arxiv.org/abs/1812.01549) and with Stephane Le Roux (https://arxiv.org/abs/1407.5587).