A general form of relative recursion

Abstract

For every partial combinatory algebra (pca) $A$ and every partial endofunction on $A$, a pca $A[f]$ is constructed such that in $A[f]$, the function $f$ is representable by an element; a universal property of the construction is formulated in terms of Longley's 2-category of pcas and decidable applicative morphisms.

10 pages, see also http://www.math.uu.nl/people/jvoosten/realizability/relrec.ps.gz