Series: Penn State Logic Seminar

Date: Tuesday, September 16, 2003

Time: 2:30 - 3:45 PM

Place: 113 McAllister Building

Speaker: Christopher Griffin, Penn State, ARL and Mathematics

Title: Coloring Infinite Cardinals: There's not a crayon big enough!

Abstract:

We will explore colorings on sets constructed from subsets of infinite 
cardinal numbers. For a fixed natural number n and a set X, [X]^n is 
the set of subsets of X of cardinality n. A coloring of [X]^n is a 
function mapping [X]^n to a (possibly infinite) set of colors C_1, C_2, 
etc. We say that a set H contained in X is homogeneous (with respect to 
a coloring f) if the coloring f is constant on [H]^n. We will 
investigate the question: Given a set X, a number n, and a coloring f 
does there exists a homogeneous set H in X of a given cardinality. 
Various Ramsey and anti-Ramsey theorems will be proved. In particular, 
we will discuss the Erdos-Rado theorem and its natural generalizations. 
We will also introduce compact cardinals and Ramsey cardinals. Time 
permitting, we will investigate the connections between the existence 
of homogeneous sets and model theoretic indiscernibles.