full size

Berkeley, CA, June 07-08, 2014

Organizers: Ralf Schindler and John Steel

Schedule:

- Saturday

1:00--2:00 Moti Gitik (Tel Aviv): TBA

2:00-3:00 Menachem Magidor (Jerusalem): TBA

3:30--4:30 Itay Neeman (Los Angeles): Higher analogues of MRP

The Proper Forcing Axiom (PFA) has played a central role in set theory since its introduction through work in the late 1970s and early 1980s. The question of whether the axiom and its applications have analogues for handling more than $\aleph_1$ constraints is of foundational importance to our understanding of the continuum. Unfortunately the countable support forcing iterations used in the original proof of the consistency of PFA cannot lead to such analogues. As a result the search for analogues was largely been dormant. But there has been a lot of progress on the question recently, sparked by finite conditions forcing notions developed by Friedman and Mitchell. In the talk we describe some of this progress, including higher analogues for Moore's Mapping Reflection Principle (a consequence of PFA) and for some of its applications.

Party at 7pm

- Sunday

10:00--11:00 Dima Sinapova (Chicago): Combinatorial properties at successors of singular cardinals

11:00--12:00 John Steel (Berkeley): The importance of being coherent

Mitchell's framework of coherent sequences of extenders is the foundation for much of inner model theory. We shall discuss one way to generalize this framework so that, granted an iterability hypothesis, it can produce inner models with partially supercompact cardinals. This is joint work with Itay Neeman, inspired in part by earlier work of Hugh Woodin in the same area.

12:00--2:00 lunch break

2:00--3:00 W. Hugh Woodin: The extent of generic absoluteness and the form of Ultimate L

Subject to fairly general constraints, the extension of the Inner Model Program to the level of one supercompact cardinal will yield an ultimate version of L. The current scenarios forecast the construction of two flavors of this ultimate L with very different properties. We discuss emerging evidence from consideration of the possible extent of generic absoluteness principles that there is in fact just one flavor.

3:00--4:00 Martin Zeman (Irvine): Weak saturation properties of the nonstationary ideal on Aleph-2

I will discuss some recent consistency results concerning the properties of the nonstationary ideal on Aleph-2 restricted to points of cofinality Aleph-1. These properties are consequences of saturation. The results generalize to any successor of a regular cardinal. This is a joint work with Sean Cox.

Poster.

Here is a list of Berkeley Hotels. For some of them, there is a University rate. People would need to make their own reservations, then email Judie Filomeo (judiew@math.berkeley.edu) about it. She would then call the hotel to get the reduced rate.

Cf. also Conference on Descriptive Inner Model Theory

Cf. also boise extravaganza in set theory (BEST 2014)