Open Access
Spring 1997 A Conjecture on Numeral Systems
Karim Nour
Notre Dame J. Formal Logic 38(2): 270-275 (Spring 1997). DOI: 10.1305/ndjfl/1039724890


A numeral system is an infinite sequence of different closed normal $\lambda$-terms intended to code the integers in $\lambda$-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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Karim Nour. "A Conjecture on Numeral Systems." Notre Dame J. Formal Logic 38 (2) 270 - 275, Spring 1997.


Published: Spring 1997
First available in Project Euclid: 12 December 2002

zbMATH: 0918.03009
MathSciNet: MR1489413
Digital Object Identifier: 10.1305/ndjfl/1039724890

Primary: 03B40
Secondary: 03D20

Rights: Copyright © 1997 University of Notre Dame

Vol.38 • No. 2 • Spring 1997
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