
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.

Novemver 11th  Grigor Sargsyan (Gdansk). Determinacy, forcing axioms and inner models.
Continuation

Novemver 18th  Grigor Sargsyan (Gdansk). Determinacy, forcing axioms and inner models.
Continuation

November 26th  Grigor Sargsyan (Gdansk). Determinacy, forcing axioms and inner models.
Update: This talk has been moved to thursday 4:15 pm!
Continuation

December 2nd  Paul Larson (Miami Univ., Oxford OH). Square principles in Pmax extensions of Chang models.
Abstract: We show that the statements \(\square(\omega_{3})\) and \(\square(\omega_{4})\) both fail in the \(\mathbb P_{\mathrm{max}}\) extension of a variation of the Chang model introduced by Sargsyan. This is joint work with Grigor Sargsyan.

December 9th  Paul Larson (Miami Univ., Oxford OH). Square principles in Pmax extensions of Chang models.
Continuation

December 16th  Paul Larson (Miami Univ., Oxford OH). Square principles in Pmax extensions of Chang models.
Continuation

January 13th  Ralf Schindler. The Stable Core.
Abstract: S. Friedman introduced the stable core, \(L[S]\), and showed that \(V\) is class generic over \(L[S]\). He also showed that \(L[S]\) is a
definable inner model of an iterate of a mouse which has a measurable
definable Woodin cardinal. We will produce versions of these results.

January 20th  Stefan Hoffelner. Forcing the \(\Pi^1_3\) Reduction Property.
Update: This talk will start at 3:30 pm.
Abstract: We continue our investigation on the forcability of regularity properties implied by projective determinacy in showing that one can force the \(\Pi^1_3\) Reduction Property over the constructible universe \(L\).

January 27th  Stefan Hoffelner. Forcing the \(\Pi^1_3\) Reduction Property.
Continuation

February 8th  Farmer Schlutzenberg. Full normalization.
Update: This talk is postponed to 5:00 pm on Monday, February the 8th.
Abstract: We will describe some aspects of full normalization for
stacks of normal iteration trees. More precisely (but somewhat
approximately), given a normal iteration strategy \(\Sigma\) for a fine
structural premouse \(M\), such that \(\Sigma\) and \(M\) both satisfy
appropriate condensation properties, we construct a strategy
\(\Sigma^*\) for transfinite stacks of iteration trees on \(M\), such that
the iterates via \(\Sigma^*\) are in fact iterates via \(\Sigma\). This is
joint work with John Steel.

February 15th  Farmer Schlutzenberg. Full normalization.
This talk starts at 5:00 pm.
Continuation.

February 23rd  Farmer Schlutzenberg. Full normalization.
This talk starts at 5:00 pm.
Continuation.

March 2nd  Farmer Schlutzenberg. Full normalization.
This talk starts at 5:00 pm.
Continuation.