Description
Book Synopsis1 Functions and Predicates.- 1. Definitions.- 2. Numerical Functions.- 3. Finitary Rules.- 4. Closure Properties.- 5. Minimal Closure.- 6. More Elementary Functions and Predicates.- 2 Recursive Functions.- 1. Primitive Recursion.- 2. Functional Transformations.- 3. Recursive Specifications.- 4. Recursive Evaluation.- 5. Church's Thesis.- 3 Enumeration.- 1. Predicate Classes.- 2. Enumeration Properties.- 3. Induction.- 4. Nondeterministic Computability.- 4 Reflexive Structures.- 1. Interpreters.- 2. A Universal Interpreter.- 3. Two Constructions.- 4. The Recursion Theorem.- 5. Relational Structures.- 6. Uniform Structures.- 5 Hyperenumeration.- 1. Function Quantification.- 2. Nonfinitary Induction.- 3. Functional Induction.- 4. Ordinal Notations.- 5. Reflexive Systems.- 6. Hyperhyperenumeration.- References.
Table of Contents1 Functions and Predicates.- §1. Definitions.- §2. Numerical Functions.- §3. Finitary Rules.- §4. Closure Properties.- §5. Minimal Closure.- §6. More Elementary Functions and Predicates.- 2 Recursive Functions.- §1. Primitive Recursion.- §2. Functional Transformations.- §3. Recursive Specifications.- §4. Recursive Evaluation.- §5. Church’s Thesis.- 3 Enumeration.- §1. Predicate Classes.- §2. Enumeration Properties.- §3. Induction.- §4. Nondeterministic Computability.- 4 Reflexive Structures.- §1. Interpreters.- §2. A Universal Interpreter.- §3. Two Constructions.- §4. The Recursion Theorem.- §5. Relational Structures.- §6. Uniform Structures.- 5 Hyperenumeration.- §1. Function Quantification.- §2. Nonfinitary Induction.- §3. Functional Induction.- §4. Ordinal Notations.- §5. Reflexive Systems.- §6. Hyperhyperenumeration.- References.
