Journal of Symbolic Logic

A Sufficient Condition for Completability of Partial Combinatory Algebras

Andrea Asperti and Agata Ciabattoni

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

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745377

Mathematical Reviews number (MathSciNet)
MR1617969

Zentralblatt MATH identifier
0918.03007

JSTOR
links.jstor.org

Citation

Asperti, Andrea; Ciabattoni, Agata. A Sufficient Condition for Completability of Partial Combinatory Algebras. J. Symbolic Logic 62 (1997), no. 4, 1209--1214. https://projecteuclid.org/euclid.jsl/1183745377


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