Imagine we have two L-structures $M$ and $N$. For each L-sentence $\phi$ , $M$ models $\phi$ iff $N$ models $\phi$. We call $M$ and $N$ two elementary equivalent L-structures.
We say $M$ and $N$ are isomorphic if there exists a function from $U_M$ to $U_N$ which is 1 to 1 and onto and preserves symbols. ( i mean an embedding which is also onto )
Now i want to prove that if two structures are isomorphic, then they are elementary equivalent.
Note : When we speak about L-formulas, we prove these kind of questions by induction on the complexity of the formulas. but in this case, we have sentences not formulas.