Logical Theories and Compatible Operations
Résumé
We survey operations on (possibly infinite) relational structures that are compatible with logical theories in the sense that, if we apply the operation to given structures then we can compute the theory of the resulting structure from the theories of the arguments (the logics under consideration for the result and the arguments might differ). Besides general compatibility results for these operations we also present several results on restricted classes of structures, and their use for obtaining classes of infinite structures with decidable theories.