Accession Number : AD0686415

Title :   REAL NUMBERS AND FUNCTIONS IN THE KLEENE HIERARCHY AND LIMITS OF RECURSIVE, RATIONAL FUNCTIONS,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Shapiro,N. Z.

Report Date : APR 1969

Pagination or Media Count : 22

Abstract : Let f be a real number. It is well known that the set of rational numbers that are less than f is a recursive set if and only if f is representable as the limit of a recursive, recursively convergent sequence of rational numbers. In this study the condition that the set of rational numbers less than f is recursive is replaced by the condition that this set is at various points in the Kleene hierarchy. The recursive, recursively convergent limit is replaced by a variety of other recursive limiting processes. (Author)

Descriptors :   (*MATHEMATICAL LOGIC, RECURSIVE FUNCTIONS), (*RECURSIVE FUNCTIONS, RATIONAL NUMBERS), REAL NUMBERS, SEQUENCES(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE