Talks during the winter of 2020/21

Novemver 4th  Grigor Sargsyan (Gdansk). Determinacy, forcing axioms and inner models.
Abstract: We will exposit some recent results of the speaker and others
that connect determinacy axioms, forcing axioms and inner models. A
culmination of this work is a recent proof that the most liberally
backgrounded construction of a model build from an extender sequence
cannot be shown to converge in ZFC alone. In this construction, which
is a type of \(K^c\) construction, one uses extenders that are certified by
a Mostowski collapse. This result challenges common perceptions of the
role of the model \(K^c\) in the inner model program.
We will mention a specific consistency result showing that the failure
of \(\square_{\omega_3}\) and \(\square(\omega_3)\) with
\(2^\omega=2^{\omega_1}=\omega_2\) and \(2^{\omega_2}=\omega_3\) is weaker than a
Woodin cardinal that is a limit of Woodin cardinals.
Many people have been involved in this project. The work is heavily
based on the efforts of Steel, Jensen, Woodin, Schindler, Mitchell,
Schimmerling, Trang, Larson, Neeman, Zeman, Schlutzenberg, the speaker
and many others.