Long Borel Games

Abstract

It is shown that Borel games of length ${\omega }^2$ are determined if, and only if, for every countable ordinal $\alpha$, there is a fine-structural, countably iterable extender model of Zermelo set theory with $\alpha$-many iterated powersets above a limit of Woodin cardinals.

arXiv comment30 pages. This version: December 2018