The Ultimate Supercompactness Measure—Logic Advanced CLass, University of Oxford, June 2024

This will be a talk for the Logic Advanced Class at the Mathematical Institute, University of Oxford. The topic concerns the extension of the axiom of determinacy \mathsf{AD}^+ as well as the axiom V = \mathsf{Ultimate}\ L. It will take place on the 13th of June 2024 at 11 AM in the lecture room C3.

Abstract. Solovay defined the inner model L(\mathbb{R}, \mu) in the context of \mathsf{AD}_{\mathbb{R}} by using it to define the supercompactness measure \mu on \mathcal{P}_{\omega_{1}}(\mathbb{R}) naturally given by \mathsf{AD}_{\mathbb{R}}. Solovay speculated that stronger versions of this inner model should exist, corresponding to stronger versions of the measure \mu. Woodin, in his unpublished work, defined \mu_{\infty} which is arguably the ultimate version of the supercompactness measure \mu that Solovay had defined. I will talk about \mu_{\infty} in the context of \mathsf{AD}^+ and the axiom V = \mathsf{Ultimate}\ L.

The event will be followed by another talk on the subject of extensions of the axiom of determinacy. Douglas Blue, from the University of Pittsburgh, will talk about The iterability problem and the transfinite generalization of AD for the Logic Seminar at the Mathematical Institute at 5PM in the lecture room L3.

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