ABSTRACT

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 level. The articles in this volume are refinements of these excellent lectures.

chapter 2|11 pages

Borelsets

chapter 3|3 pages

Borel equivalence relations

chapter 4|7 pages

Infinitary logic

chapter 5|4 pages

Scott’s analysis

chapter 6|4 pages

Glimm-Effros

chapter 7|7 pages

Final theorem

chapter 8|1 pages

More reading

chapter |1 pages

REFERENCES

chapter 1|1 pages

Introduction

chapter 2|4 pages

Definitions, preliminary results

chapter 3|6 pages

The theory ACFA

chapter 4|11 pages

σ-closed sets, independence, and SU-rank

chapter 5|3 pages

Study of the fixed field

chapter 6|7 pages

Orthogonality and modularity

chapter 7|7 pages

Groups, generic types, stabilizers

chapter 8|11 pages

General results about models of ACFA

chapter 1|1 pages

Introduction

chapter 2|3 pages

Reals, computable or otherwise

chapter 3|2 pages

Other classes of reals

chapter 5|4 pages

Presentations of reals

chapter 6|2 pages

Kolmogorov complexity

chapter 7|1 pages

Prefix-free complexity

chapter 8|4 pages

Complexity of reals

chapter 9|4 pages

Relative randomness

chapter 11|5 pages

Other measures of relative randomness

chapter 12|7 pages

≤K, ≤c , and ≤T

chapter 13|5 pages

Other areas

chapter |3 pages

REFERENCES

chapter 1|1 pages

Introduction

chapter 2|2 pages

Open induction

chapter 3|4 pages

Bounded induction

chapter 4|3 pages

Exponentiation

chapter 5|3 pages

McAloon’s theorem

chapter 6|2 pages

Pigeonhole principle

chapter 7|3 pages

Chebyshev’s theorem

chapter 8|10 pages

Pell equations

chapter 9|5 pages

Residue fields