# Accession Number:

## AD0684607

# Title:

## ON PRIMITIVE RECURSIVE PERMUTATIONS AND THEIR INVERSES,

# Descriptive Note:

# Corporate Author:

## CALIFORNIA UNIV IRVINE DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 1969-01-01

# Pagination or Media Count:

## 12.0

# Abstract:

It is known that there is a primitive recursive permutation of the nonnegative integers whose inverse is recursive but not primitive recursive. Robinson showed that every singulary recursive function f is representable as f AB superscript -1C, where A, B, C are primitive recursive and B is a permutation. This report presents a sharper version of Robinsons result, that is, every singulary recursive f is of the form f AB superscript -1C for fixed A,C where A,B,C are elementary functions and B is a permutation. The proof employs meta-mathematical methods. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics