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A sufficient condition for completability of partial combinatory algebras

Published online by Cambridge University Press:  12 March 2014

Andrea Asperti  and
Agata Ciabattoni
Andrea Asperti
Affiliation:
Dipartimento di Matematica, P.Zza di Porta S.Donato 5, Bologna, Italy E-mail: asperti@cs.unibo.it
Agata Ciabattoni
Affiliation:
Corso di Laurea in Scienze dell'Informazione, Università degli Studi di Bologna, Via Sacchi 3, Cesena, Italy E-mail: agata@csr.unibo.it
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Abstract

A Partial Combinatory Algebra is completable if it can be extended to a total one. In [1] it is asked (question 11, posed by D. Scott, H. Barendregt, and G. Mitschke) if every PCA can be completed. A negative answer to this question was given by Klop in [12, 11]; moreover he provided a sufficient condition for completability of a PCA (M, •, K,S) in the form of ten axioms (inequalities) on terms of M. We prove that just one of these axiom (the so called Barendregt's axiom) is sufficient to guarantee (a slightly weaker notion of) completability.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 4 , December 1997 , pp. 1209 - 1214
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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