Generally meeting (unless otherwise noted):- UCLA, MS 3915D, Fridays, 2-3:30pm.
We will start October 19. Clinton Conley will speak on Defining small sets from intersecting families:
October 26, November 2: Yiannis Souldatos: Cardinals that are characterizable by Scott sentences
November 9: Andrie Nies Borel presentable structures
Abstract:
Traditionally, effectivity is studied for countable structures. Borel
structures in contrast allow us to develop a theory of effectivity for
the equally natural uncountable structures, such as the field of real
numbers. After some initial work by Friedman (1979), the forthcoming
paper entitled "From automatic structures to Borel structures'' by
Khoussainov, Hjorth, Montalban and myself has revived the subject by
applying Borel structures to solve a well-known question on Buechi
presentable structures; see Section 5 of Nies' Bull. Symb. Logic paper
"Describing Groups'', Sept 2007. We show that there is a Buechi
presentable structure without an injective Buechi representation.
Further, there exists a Rabin presentable structure that is not
Borel.
November 16: Greg Hjorth will speak on Equivalence relations with many ends and percolation theory.
November 30: Dima Sinapova will speak on A model with a very good scale and a very bad scale.
Given a supercompact cardinal $\kappa$ and a regular cardinal
$\lambda<\kappa$, we describe a type of forcing such that in the
generic extension the cofinality of $\kappa$ is $\lambda$, there is
a very good scale at $\kappa$, a bad scale at $\kappa$, and SCH at
$\kappa$ fails.