## Journal of Symbolic Logic

### On the Existence of Extensional Partial Combinatory Algebras

Ingemarie Bethke

#### Abstract

The principal aim of this paper is to present a construction method for nontotal extensional combinatory algebras. This is done in $\S2$. In $\S0$ we give definitions of some basic notions for partial combinatory algebras from which the corresponding notions for (total) combinatory algebras are obtained as specializations. In $\S1$ we discuss some properties of nontotal extensional combinatory algebras in general. $\S2$ describes a "partial" variant of reflexive complete partial orders yielding nontotal extensional combinatory algebras. Finally, $\S3$ deals with properties of the models constructed in $\S2$, such as incompletability, having no total submodel and the pathological behaviour with respect to the interpretation of unsolvable $\lambda$-terms.

#### Article information

Source
J. Symbolic Logic, Volume 52, Issue 3 (1987), 819-833.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742447

Mathematical Reviews number (MathSciNet)
MR902995

Zentralblatt MATH identifier
0645.03010

JSTOR