Algebraic Computability and Enumeration Models:

Recursion Theory and Descriptive Complexity

Smullyan, R., 1993,

Recursion Theory for Metamathematics, Oxford University Press, Nueva York.

Computability theory; an introduction to recursion theory.

of California, Los Angeles) has written a clear, focused, and surprisingly literate textbook--it is a rare mathematician who is this adept with words--describing the history and theory of recursion theory that will be ideal for one-semester advanced courses in mathematics and computer science.

Trained in theoretical linguistics and

recursion theory, Hennix was saying that you need an algorithm to achieve a distinguished result.

Theoretical computer scientists, whether professional or in training, will find this collection of written versions of 20 talks given at the June-August 2005 workshop especially useful for such study areas as

recursion theory and set theory.

Judging from

recursion theory, living things only have one level.

* Recursion: primitive recursion (for loops) and general recursion (while loops) were introduced in

recursion theory and are pervasive in modern high-level languages.

It is, perhaps, the most sophisticated technically, drawing on the theory of inductive definitions, various results in

recursion theory, and techniques involving possible world semantics.

Recursion Theory: Computational Aspects of Definability

Material is arranged in chapters on predicate logic, axiomatic set theory,

recursion theory and computability, Godel's incompleteness theorems, model theory, contemporary set theory, nonstandard analysis, and constructive mathematics.

The authors begin by covering the development of Peano arithmetic, mathematical induction and

recursion theory. They then discuss integers, rings and ordered integral domains.