Journal of Symbolic Logic

A Sufficient Condition for Completability of Partial Combinatory Algebras

Andrea Asperti and Agata Ciabattoni

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.


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 $(M, \cdot, K, S)$ 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.

Article information

J. Symbolic Logic, Volume 62, Issue 4 (1997), 1209-1214.

First available in Project Euclid: 6 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Asperti, Andrea; Ciabattoni, Agata. A Sufficient Condition for Completability of Partial Combinatory Algebras. J. Symbolic Logic 62 (1997), no. 4, 1209--1214.

Export citation