ABSTRACT

This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.

chapter 1|2 pages

Computability

chapter 2|2 pages

Functions and Relations

chapter 3|3 pages

The Basic Machine

chapter 4|4 pages

Macros

chapter 5|4 pages

Closure Properties

chapter 6|6 pages

Definitions of Recursive Functions

chapter 7|5 pages

Codes

chapter 8|7 pages

Indices

chapter 9|3 pages

Church’s Thesis

chapter 10|5 pages

Word Problems

chapter 11|8 pages

Undecidable Theories

chapter 12|5 pages

Relative Recursion

chapter 13|6 pages

The Arithmetical Hierarchy

chapter 14|6 pages

Recursively Enumerable Relations

chapter 15|7 pages

Degrees

chapter 16|4 pages

Evaluation of Degrees

chapter 17|5 pages

Large RE Sets

chapter 18|5 pages

Function of Reals

chapter 19|4 pages

The Analytical Hierarchy

chapter 20|5 pages

The Projective Hierarchy