There is a consensus, that "isomorphy" (the "is isomorphic to"-relation) is the right kind of sameness between universal algebras (say groups, (single-sorted) vector spaces, lattices, ...), because isomorphic objects share all their "algebraic properties". I wonder though:
Is there a (meta)theorem, that tells us exactly which properties, I can possibly come up with in the language of said algebraic structure, are indeed shared by isomorphic algebras?
If not, is there at least a general (meta)theorem stating, that a big class of (which?) properties are shared by isomorphic algebras?
This question might be related to model theory, although I have to say I know nothing about that.