Elementary Pairs of Primitive Normal Theories

The main objective of the paper is proving that classes of primitive normal, primitive bound, antiadditive, and additive theories are closed under $P$-expansions. This phenomenon is quite remarkable, for the main “structure” classes of theories studied within model theory (such as stable, totally transcendental, etc.) do not possess such a property. Furthermore, it is proved that primitive bound theories are $P$-stable, and we furnish an example of a primitive bound theory with models that are not primitive bound.