A conjecture on numeral systems

Details A conjecture on numeral systems A conjecture on numeral systems

2009-05-06

arxiv.org/abs/0905.0755v1

Notre Dame Journal of Formal Logic 38 (1997) 270-275

Mathematics

Logic

Scientific paper

A numeral system is an infinite sequence of different closed normal $\lambda$-terms intended to code the integers in $\lambda$-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.

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