Expressive Power of Query Languages for Constraint Complex Value Databases

Motivated by constraint complex values which allow us to represent nested finitely representable sets, we study the expressive power of various query languages over constraint complex value databases. The tools we use come in the form of collapse results which are well established results in the context of first-order logic. We show that activegeneric collapse carries over to second-order logic for structures with o-minimality and any relational signature in the complex value model. We also consider the problem of safety in the context of embedded finite complex value models and constraint complex value databases.