General Recursion Theory: An Axiomatic Approach

Contents
Pons Asinorum
Chapter 0. On the Choice of Correct Notions for the General Theory
	0.1 Finite Algorithmic Procedures
	0.2 FAP and Inductive Definability
	0.3 FAP and Computation Theories
	0.4 Platek\'s Thesis
	0.5 Recent Developments in Inductive Definability
Part A. General Theory
	Chapter 1. General Theory: Combinatorial Part
		1.1 Basic Definitions
		1.2 Some Computable Functions
		1.3 Semicomputable Relations
		1.4 Computing Over the Integers
		1.5 Inductively Defined Theories
		1.6 A Simple Representation Theorem
		1.7 The First Recursion Theorem
	Chapter 2. General Theory: Subcomputations
		2.1 Subcomputations
		2.2 Inductively Defined Theories
		2.3 The First Recursion Theorem
		2.4 Semicomputable Relations
		2.5 Finiteness
		2.6 Extension of Theories
		2.7 Faithful Representation
Part B. Finite Theories
	Chapter 3. Finite Theories on One Type
		3.1 The Prewellordering Property
		3.2 Spector Theories
		3.3 Spector Theories and Inductive Definability
	Chapter 4. Finite Theories on Two Types
		4.1 Computation Theories on Two Types
		4.2 Recursion in a Normal List
		4.3 Selection in Higher Types
		4.4 Computation Theories and Second Order Definability
Part C. Infinite Theories
	Chapter 5. Admissible Prewellorderings
		5.1 Admissible Prewellorderings and Infinite Theories
		5.2 The Characterization Theorem
		5.3 The Imbedding Theorem
		5.4 Spector Theories Over ω
	Chapter 6. Degree Structure
		6.1 Basic Notions
		6.2 The Splitting Theorem
		6.3 The Theory Extended
Part D. Higher Types
	Chapter 7. Computations Over Two Types
		7.1 Computations and Reflection
		7.2 The General Plus-2 and Plus-1 Theorem
		7.3 Characterization in Higher Types
	Chapter 8. Set Recursion and Higher Types
		8.1 Basic Definitions
		8.2 Companion Theory
		8.3 Set Recursion and Kleene-recursion in Higher Types
		8.4 Degrees of Functional
		8.5 Epilogue
References
Notation
Author Index
Subject Index