### Logic in Southern California

Caltech

#### Saturday, March 8, 2014

2:00 – 6:00 pm

Sloan room 151

#### Funded by NSF grant DMS-1044150

### Schedule:

2:00-3:00 Erik Walsberg (UCLA)

3:15-4:15 Henry Macdonald (Caltech)

4:15-5:00 Coffee Break

5:00-6:00 Andres Forero (UCI)

Abstracts:

**Talk Title:** Metric geometry in the O-minimal setting.

**Abstract:** I will discuss the geometry of those metric spaces which are definable in o-minimal expansions of fields.

**Henry Macdonald (Caltech). **

**Talk Title:** Descriptive combinatorics

**Abstract:** In combinatorics, the axiom of choice is often used to justify the existence of a certain object – a graph coloring, say, or a matching. In descriptive combinatorics, we ask: what happens if we place definability restrictions from descriptive set theory on these objects? I will discuss various situations where these considerations give rise to some interesting questions. In particular, I will discuss “Borel chromatic numbers”, and a result about extending a combinatorial argument from cardinal arithmetic to the field of Borel equivalence relations.

**Talk Title:** Consistency strength of Stationary Catching

**Abstract:** In this talk we will give a brief overview of Generic large cardinal axioms and their motivation. In concrete we consider certain collections of structures that behave nicely with respect to a fixed ideal on omega_2, and introduce axioms asserting that these collections are large. We will specifically consider the consistency strength of the Stationary Catching Axiom (which is a weakening of the saturation of an ideal), in terms of Woodin cardinals. For this purpose, we will describe two important techniques used: the core model induction, and covering arguments.