## elementary anti-equivalence?

I wasn't sure where to post this question. Please move it if you think it belongs in the logic forum.

Elementary equivalence is weaker than being isomorphic. We can easily define an analogous weaker condition for anti-isomorphisms (at least in the case of typical algebraic structures) by demanding that every first-order statement in one structure be true in the other but with the order of operations reversed.

Is there a name for such a condition?