On Simple Goedel Numberings and Translations

Abstract

In this paper we consider Goedel numberings (viewed as simple models for programming languages) into which all other Goedel numberings can be translated very easily. Several such classes of Goedel numberings are defined and their properties are investigated. We also compare these classes of Goedel numberings to optimal Goedel numberings and show that translation into optimal Goedel numberings can be computationally arbitrarily complex.