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.
: 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.