In fall 2000, the Notre Dame logic community hosted Greg Hjorth, Rodney G. Downey, Zoe Chatzidakis, and Paola D'Aquino as visiting lecturers. Each of them presented a month-long series of expository lectures at the graduate lecture. The articles in this volume are refinements of these excellent lectures. Hjorth's article provides an introduction to current work on Borel and equivalent classes using countable model theory as the motivating example. Chatzidakis's article is an introduction to the model theory of difference fields: a field with a distinguished automorphism. Results from the model theory of difference fields have been recently been used by Hrushovski and other model theorist to show various results in number theory. Downey's contribution provides an introduction to the recent work by him and many others on the relationship between randomness and computably enumerable reals. Paola D'Aquino studies weak models of Peano Arithmetic (in particular, models where induction is restricted to bounded formulas) focusing on number theoretic results.

In fall 2000, the Notre Dame logic community hosted Greg Hjorth, Rodney G. Downey, ZoA(c) Chatzidakis, and Paola D'Aquino as visiting lecturers. Each of them presented a month long series of expository lectures at the graduate level. The articles in this volume are refinements of these excellent lectures.