Formalized Recursive Functionals And Formalized Realizability

Formalized Recursive Functionals and Formalized Realizability

This monograph carries out the program which the author formulated in earlier work, the formalization of the theory of recursive functions of type 0 and 1 and of the theory of realizability.

Classical Recursion Theory

1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.

Metamathematical Investigation of Intuitionistic Arithmetic and Analysis