Abstract:
Preface -- 1. The complexity of sets -- 2. The descriptive complexity of strings -- 3. Martin-Lof randomness and its variants -- 4. Diagonally noncomputable functions -- 5. Lowness Properties and K-triviality -- 6. Some advanced computability theory -- 7. Randomness and betting strategies -- 8. Classes of computational complexity -- 9. Higher computability and randomness -- Solutions to exercises -- References -- Index