Partial Representations and Partial Group Algebras

Stability of representations of effective partial algebras

An algebra is effective if its operations are computable under some numbering. When are two numberings of an effective partial algebra equivalent? For example, the computable real numbers form an effective field and two effective numberings of the field of computable reals are equivalent if the limit operator is assumed to be computable in the numberings (theorems of Moschovakis and Hertling). ...

Collapsing Partial Combinatory Algebras

Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or re-cursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identiication of elements in a pca. We establish several facts concerning nal collapses (maximal identiication of elements). `En passan...

Extending partial combinatory algebras

Disjoint-union partial algebras

Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are defined. We provide a recursive first-order axiomatisation of the class of partial algebras isomorphic to a disjointunion partial algebra of sets but prove that ...

Limiting partial combinatory algebras

We $\mathrm{w}\mathrm{i}\mathrm{u}$ construct from every partial