Products of Classes of Finite Structures

We study the preservation of certain properties under products of classes of finite structures. In particular, we examine age indivisibility, indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We explore how each of these properties interact with the wreath product, direct product, and free superposition of classes of structures. Additionally, we consider the classes of theories which admit configurations indexed by these products.Comment: 33 page