In this course, we will investigate particular infinite games — Ulam style cut and choose games and variants of the precipitous game — and how the existence of winning strategies for particular players in these games is connected to generic large cardinals, and to the existence of large cardinals. The main results of this course will show how to obtain, starting from large cardinals, winning strategies in these games on small cardinals, and on the other hand, how to obtain (generic) large cardinals from winning strategies in these games.
Verification
In-depth study of the student
Prerequisites
We will only assume some knowledge of basic set theory and some very basic knowledge about the forcing technique.
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