Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 52, Issue 3 (1987), 819-833.
On the Existence of Extensional Partial Combinatory Algebras
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.
J. Symbolic Logic, Volume 52, Issue 3 (1987), 819-833.
First available in Project Euclid: 6 July 2007
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Bethke, Ingemarie. On the Existence of Extensional Partial Combinatory Algebras. J. Symbolic Logic 52 (1987), no. 3, 819--833. https://projecteuclid.org/euclid.jsl/1183742447