Logical Methods in Computer Science. DOI: 10.2168/LMCS-3(1:2).
Cleaner proofs and additional results around cores can be found in the journal version of my paper with and titled On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction. The key technique for the simplification of the proofs is the concept of existential positive closure . With this concept, one can develop a theory or core companions that is analogous to the classical theory of model companions. It is then easy to derive the results in my paper on cores of countably categorical structures from those more general results.