During the second week, we will be at the TU Wien Freihaus. It is located at Wiedner Hauptstaße 8–10, 1040 Wien.
The talks will take place in Zeichensaal 3, green area, 7th floor and the coffee breaks will be at the meeting room, green area, 5th floor.
| Monday, July 1 | Tuesday | Wednesday | Thursday | Friday, July 5 | |
|---|---|---|---|---|---|
| 09:45-10:00 | -Coffee- | -Coffee- | -Coffee- | -Coffee- | -Coffee- |
| 10:00-11:00 | Nam Trang (1/5) | Farmer Schlutzenberg (2/5) | Gabriel Goldberg (3/5) | Nam Trang (4/5) | Farmer Schlutzenberg (4/5) |
| 11:00-11:30 | -Coffee- | -Coffee- | -Coffee- | -Coffee- | -Coffee- |
| 11:30-12:30 | Farmer Schlutzenberg (1/5) | Gabriel Goldberg (2/5) | Nam Trang (3/5) | Nam Trang (5/5) | Farmer Schlutzenberg (5/5) |
| 12:30-14:00 | -Lunch- | -Lunch- | -Lunch- | -Lunch- | -Lunch- |
| 14:00-15:00 | Gabriel Goldberg (1/5) | Nam Trang (2/5) | Farmer Schlutzenberg (3/5) | Gabriel Goldberg (4/5) | Gabriel Goldberg (5/5) |
| 15:00-17:00 | -informal work groups- | -informal work groups- | -informal work groups- | -informal work groups- | -informal work groups- |
On the afternoons of the second week, informal working groups will take place in smaller groups. Anyone who has an idea can start a group. Please let us know before or during the conference if you have an idea for a topic.
| What? | Who? | When? | Where? |
|---|---|---|---|
| least disagreement strategy comparison | John Steel | tba | tba |
Strong Mouse Capturing is the statement: for any hod pair or an sts hod pair (P, Σ) such that Σ has strong branch condensation and is strongly fullness preserving, and for any reals x, y, x is ordinal definable from Σ and y if and only if x is in some Σ-mouse over y. We outline a proof of Strong Mouse Capturing in natural models of AD+ (i.e. those of the form V = L(P(R))) up to the minimal model of LSA. Basic terminology and definitions concerning hod mice are from Sargsyan’s “Hod mice and the mouse set conjecture” and Sargsyan-Trang’s “The Largest Suslin Axiom”.
We will discuss a process for extending a normal iteration strategy Sigma to an iteration strategy Gamma for transfinite stacks of normal trees, assuming that Sigma has a certain natural condensation property. Every iterate produced by Gamma will also be a (normal) iterate produced by Sigma. This is a combination of work of John Steel and the author.
Reference: “Full normalization for transfinite stacks”, arXiv:2102.03359
The subject of this tutorial is Woodin’s HOD conjecture, one of the most prominent open problems in pure set theory. We begin with a proof of his HOD dichotomy theorem along with an improvement of the speaker’s reducing the large cardinal hypothesis from an extendible to a strongly compact cardinal. Following this, we mostly discuss the implications of the failure of the HOD conjecture, especially $\omega$-strongly measurable cardinals and a condition under which such cardinals are locally supercompact in $\HOD$.