### Graduate Student Seminar, 4:00 pm April 16, 2007; HH229

#### Speaker:

Josh Cole

#### Title:

Decidable and Undecidable Theories

#### Abstract:

We say that the theory of a class of mathematical structures is "decidable" if
there is an algorithm for determining which first-order sentences are true of
all structures in the class. I will make this definition more precise and give
examples of both decidable and undecidable theories of familiar classes
of mathematical structures. The class of groups will be given special attention;
I will show how the existence of a finitely presented group with an unsolvable
word problem implies that the theory of the class of groups is undecidable.

To volunteer to give a talk, or for any other questions regarding this schedule,
contact Sara Miller