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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.
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Novemver 11th - Grigor Sargsyan (Gdansk). Determinacy, forcing axioms and inner models.
Continuation
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Novemver 18th - Grigor Sargsyan (Gdansk). Determinacy, forcing axioms and inner models.
Continuation
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November 26th - Grigor Sargsyan (Gdansk). Determinacy, forcing axioms and inner models.
Update: This talk has been moved to thursday 4:15 pm!
Continuation
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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.
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December 9th - Paul Larson (Miami Univ., Oxford OH). Square principles in Pmax extensions of Chang models.
Continuation
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December 16th - Paul Larson (Miami Univ., Oxford OH). Square principles in Pmax extensions of Chang models.
Continuation
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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.
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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 \(L\).
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January 27th - Stefan Hoffelner. Forcing the \(\Pi^1_3\) Reduction Property.
Continuation
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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.
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February 15th - Farmer Schlutzenberg. Full normalization.
This talk starts at 5:00 pm.
Continuation.
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February 23rd - Farmer Schlutzenberg. Full normalization.
This talk starts at 5:00 pm.
Continuation.
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March 2nd - Farmer Schlutzenberg. Full normalization.
This talk starts at 5:00 pm.
Continuation.