Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identification of elements in a pca. We establish several facts concerning final collapses (maximal identification of elements). `En passant' we find another example of a pca that cannot be extended to a total one.

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Department of Computer Science [CS]
Specification and Analysis of Embedded Systems

Bethke, I, & Klop, J.W. (1995). Collapsing partial combinatory algebras. Department of Computer Science [CS]. CWI.