Philipp Schlicht (University of Bristol)

Interaction of determinacy and forcing

Note room change: Roger Stevens LT 08 (9.08)

Determinacy principles provide a unified theory of definable sets of reals beyond Borel and analytic sets, while forcing is an important technique to study the independence of properties of sets of reals. This suggests studying the interaction of the two: how robust are determinacy principles under well behaved forcings? I will talk about the history of this problem as well as recent joint results with Jonathan Schilhan and Johannes Schürz on iterations of proper forcings. A sample application of our results is the following: starting from a model of analytic determinacy, one can construct a model of analytic determinacy and the Borel conjecture.

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