Prove that Multiplication is not explicitly definable in $\mathfrak{M}=\langle R, < , + \rangle$.
I started with $F(x)=2x$ and I basically need to show it is an automorphism of $\mathfrak{M}$
And then I think it would be easiest to assume it is explicitly definable and try to get a contradiction by using the automorphism theorem. But I do not know how to proceed and show the automorphism.