NiesBookWithErrata

ContentsxvWell-orders and computable ordinals 367Representing Π 1 1 relations by well-orders 367Π 1 1 classes and the uniform measure 369Reducibilities 370A set theoretical view 3719.2 Analogs of Martin-Löf randomness and K-triviality 372Π 1 1 Machines and prefix-free complexity 373A version of Martin-Löf randomness based on Π 1 1 sets 376An analog of K-triviality 376Lowness for Π 1 1-ML-randomness 3779.3 ∆ 1 1-randomness and Π 1 1-randomness 378Notions that coincide with ∆ 1 1-randomness 379More on Π 1 1-randomness 3809.4 Lowness properties in higher computability theory 381Hyp-dominated sets 381Traceability 382Solutions to the exercises 385Solutions to Chapter 1 385Solutions to Chapter 2 389Solutions to Chapter 3 391Solutions to Chapter 4 393Solutions to Chapter 5 395Solutions to Chapter 6 399Solutions to Chapter 7 400Solutions to Chapter 8 402Solutions to Chapter 9 408References 410Notation Index 418Index 423