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Logic Seminar

The Ultrapower Axiom

 Gabriel Goldberg, Harvard University

Location:  HILL 705
Date & time: Monday, 27 November 2017 at 5:00PM - 6:00PM

Abstract:  The Ultrapower Axiom (UA) is a set theoretic principle that holds in all known canonical inner models, generalizing the linearity of the Mitchell order on normal ultrafilters to all countably complete ultrafilters. If UA can be refuted by any large cardinal axiom whatsoever, this rules out using anything like the current methodology to construct canonical inner models with even a single supercompact cardinal. Developing the theory of large cardinals assuming UA therefore leads to some insight into the inner model problem, and this talk will focus on two results in this theory: that GCH holds above the least supercompact cardinal, and that the least strongly compact cardinal is supercompact.

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