Before revision:  First, it allows us to show that a (hereditary) class of matrices on a finite alphabet either contains at least n! matrices of size n \times n, or at most c^n for some constant c.
After revision:  First, it allows us to show that a (hereditary) class of matrices over a finite alphabet either contains at least n! matrices of size n \times n, or at most c^n for some constant c.