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The decidability of hindley's axioms for strong reduction

Published online by Cambridge University Press:  12 March 2014

Bruce Lercher
Bruce Lercher*
Affiliation:
State University of New York at Binghamton
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Extract

In his paper [3] Hindley shows that strong reduction in combinatory logic (see [1] for the basic discussion of this notion) cannot be axiomatized with a finite number of axiom schemes, and then he presents an infinite system of axiom schemes for strong reduction. Hindley lists one axiom and six axiom schemes, together with a method (clause (viii) below) for generating further axiom schemes from these. The results of this note are that different applications of clause (viii) yield different axiom schemes, and that the property of being an axiom is decidable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 2 , August 1967 , pp. 237 - 239
Copyright
Copyright © Association for Symbolic Logic 1967

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References

[1]Curry, H. B. and Feys, R., Combinatory logic, vol. I, North-Holland Co., Amsterdam, 1958.Google Scholar
[2]Curry, H. B., Combinatory logic, vol. II, in preparation.Google Scholar
[3]Hindley, R., Axioms for strong reduction in combinatory logic, this Journal, vol. 32 (1967), pp. 224–236.Google Scholar