THE TWELFTH COLLOQUIUMFEST

Speaker: Pawel Gladki (Silesian University, Katowice, Poland)

Title: Quotients of spaces of orderings

Abstract:
We shall investigate quotient structures and quotient spaces of a
space of orderings arising from subgroups of index two. We provide
necessary and sufficient conditions for a quotient structure to be a
quotient space that, among other things, depend on the stability index
of the given space. The case of the space of orderings of the field $
\Q(x)$ is particularly important, since then the theory developed
simplifies significantly. A part of the theory firstly developed for
quotients of index 2 generalizes in an elegant way to quotients of
index $2^n$ for arbitrary finite $n$. Numerous examples are provided.
This is joint work with Bill Jacob and Murray Marshall.