A conjecture on numeral systems
Logic
2009-05-07 v1
Abstract
A numeral system is an infinite sequence of different closed normal -terms intended to code the integers in -calculus. H. Barendregt has shown that if we can represent, for a numeral system, the functions : Successor, Predecessor, and Zero Test, then all total recursive functions can be represented. In this paper we prove the independancy of these particular three functions. We give at the end a conjecture on the number of unary functions necessary to represent all total recursive functions.
Keywords
Cite
@article{arxiv.0905.0755,
title = {A conjecture on numeral systems},
author = {Karim Nour},
journal= {arXiv preprint arXiv:0905.0755},
year = {2009}
}