Logic in Southern California Caltech, March 8, 2014

Logic in Southern California

Saturday, March 8, 2014
2:00 – 6:00 pm
Sloan room 151

Funded by NSF grant DMS-1044150




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)

Erik Walsberg (UCLA).

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.

Andres Forero (UCI).

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.

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