Partial morphisms in categories of effective objects (Q1109126)

The paper discusses in great length the category GEN of so-called generalized numbered sets and effective morphisms. Depending on a fairly general parameter L, an object in GEN is a set X which comes equipped with a directed set of suitable ``L-computable'' partial functions of X into X whose images cover X. GEN is finally exhibited as the quasitopos of separated presheaves w.r.t. a suitable Grothendieck topology. \(\{\) There are close interrelationships of this paper with \textit{G. Rosolini}'s Ph. D. thesis [Continuity and Effectiveness in Topoi'' (Oxford, 1986)\(\}\).