**LOGIC
IN SOUTHERN CALIFORNIA
**

Saturday, November 16, 2013

**UCLA Math Sciences 6627**

**Funded
by NSF Grant DMS-1044604**

**Schedule:**

2:00 - 3:00 Jay Williams (Caltech), Group theory and countable Borel equivalence relations.

3:30 - 4:30 Trevor Wilson (UC-Irvine), Trees and generic absoluteness.

5:00 - 6:00 Spencer Unger (UCLA), The tree property.

**Abstracts**
**Driving
directions and parking** **Organizers
Previous
meetings**

Jay Williams: **Group theory and countable Borel equivalence relations**.

**Abstract:**
The theory of Borel equivalence relations gives us a way to compare the
complexity of classification problems throughout mathematics.
We will discuss classification problems from group theory and how they
fit in this framework. In particular, we will look at what makes
isomorphism of finitely generated groups special among countable
Borel equivalence relations, and explore some related results.

Trevor Wilson: **Trees and generic absoluteness**.

**Abstract:**
Generic absoluteness is a phenomenon in set theory whereby some mathematical
truths are "necessary" rather than being contingent on the actual world of
sets. More precisely, a generically absolute statement is one whose truth
or falsity is unaffected by the method of forcing, which was introduced by
Cohen to describe a possible world in which the continuum hypothesis fails.
A basic example of a generically absolute statement is, for a given tree
T of finite sequences, the statement that T has an infinite branch.
In this talk, I will discuss the extent to which other generic absoluteness
phenomena can be reduced to instances of this basic example by building
appropriate trees.

Spencer Unger: **The tree property**.

**Abstract:**
The set theoretic notion of tree property arises as a generalization to
uncountable cardinals of the classical Konig infinity lemma.
In this talk I will discuss how questions about the tree property can be
answered with the modern set theoretic tools of inner models, forcing,
and large cardinals.

Driving directions and parking:

From the 405 North

- Take 405 (San Diego Freeway) to Wilshire Blvd. East
- Travel east three blocks to Westwood Blvd.
- Turn Left on Westwood Blvd.
- Travel five blocks to Information & Parking Booth

From the 405 South

- Take 405 (San Diego Freeway) to Sunset East
- Take Sunset east to Westwood Plaza
- Turn right on Westwood Plaza
- Proceed straight to Information & Parking Booth

From the east via the 10 (Santa Monica Freeway)

- Take 10 (Santa Monica Freeway) to 405 (San Diego Freeway) North
- Take 405 (San Diego Freeway) to Wilshire Blvd. East
- Travel east three blocks to Westwood Blvd.
- Turn left on Westwood Blvd.
- Travel five blocks to Information & Parking Booth

To park on campus you will need to purchase a daily parking permit at the Information & Parking Booth. The nearest parking lots to the Department of Mathematics are 9, 6, 8, and 2.

Organizers: Alexander Kechris, Itay Neeman, Martin Zeman

**UCLA, May
12, 2012**