Speaker: Gabriel Goldberg
University of California Berkeley
Will give a Logic Seminar entitled:
AD and UA
Abstract: This talk concerns a structural resemblance between canonical inner models of large cardinal axioms (i.e., generalizations of Godel's constructible universe) and natural inner models of the Axiom of Determinacy (i.e., extensions of L(R)). Although the theories of these models are known to be deeply intertwined, their internal structure, at first glance, could appear more different: most notably, canonical inner models satisfy extremely strong forms of the Axiom of Choice, while determinacy models suffer from extravagant failures of it. A closer look reveals a series of striking analogies between the two classes of models, leading to the conjecture that both classes satisfy the Ultrapower Axiom (UA), a combinatorial principle motivated by the search for canonical inner models containing supercompact cardinals. I will sketch a proof of this conjecture up to $\aleph_{\omega }$. This is joint work with Steve Jackson.
Date: 03-04-2025
Time: 2:00 pm
Location: 125 Hayes-Healy Bldg