A Conjecture on Numeral Systems

Notre Dame Journal of Formal Logic 38 (2):270-275 (1997)
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Abstract

A numeral system is an infinite sequence of different closed normal -terms intended to code the integers in -calculus. 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 three particular 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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References found in this work

The lambda calculus: its syntax and semantics.Hendrik Pieter Barendregt - 1981 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co..
Opérateurs de mise en mémoire et traduction de Gödel.Jean-Louis Krivine - 1990 - Archive for Mathematical Logic 30 (4):241-267.

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