Summary: Some Results in Logic and Ergodic Theory
Jeremy Avigad (Chair)
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy.
Copyright c 2008 Henry Towsner
Firstly, I am grateful to the many people who took the time to read various parts of this
thesis and provide helpful suggestions and corrections: Tim Austin, James Cummings, Philipp
Gerhardy, John Griesmer, Ulrich Kohlenbach, Bryna Kra, and Terence Tao. Thanks also to
my thesis committee members, James Cummings, Ernest Schimmerling, and Stephen Simpson.
Additionally, I am grateful to the mathematics department at CMU, including Bill Hrusa,
as well as Stella, Ferna, and Nancy, for all their help over the last five years.
I also wish to thank Grisha Mints, without whose support I would never have begun this
project. Most of all, I wish to thank my advisor, Jeremy Avigad, who has been a source of