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On the Existence of Extensional Partial Combinatory Algebras
The Journal of Symbolic Logic
Vol. 52, No. 3 (Sep., 1987), pp. 819-833
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2274368
Page Count: 15
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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 λ-terms.
The Journal of Symbolic Logic © 1987 Association for Symbolic Logic