The reducts of equality up to primitive positive interdefinability

摘要

We initiate the study of reducts of relational structures up to primitivepositive interdefinability: After providing the tools for such a study, weapply these tools in order to obtain a classification of the reducts of thelogic of equality. It turns out that there exists a continuum of such reducts.Equivalently, expressed in the language of universal algebra, we classify thoselocally closed clones over a countable domain which contain all permutations ofthe domain.