Sufficient conditions for effective translation of locally generic queries

This paper continues investigations into the database of queries of first-order language theory. It is known that for many decidable theories, the collapse result holds: each locally generic query is equivalent to some restricted query. But, until now, the problem of effective construction of this query remains almost unexplored. We use earlier results of the author on the construction of a method of effective obtaining this query. The method is rather general and applicable, for example, to the Presburger arithmetic and the real number theory.