Random Graph: Stronger logic but with the zero one law

We find a logic really stronger than first order for the random graph with edge probability $\frac{1}{2}$ but satisfies the 0-1 law. This means that on the one hand it satisfies the 0-1 law, e.g. for the random graph ${\mathcal G}{n,1/2}$andontheotherhandthereisaformula$\varphi(x)$ such that for no first order $\psi (x)$ do we have: for every random enough ${\mathcal G}{n,1/2}$theformulas$\varphi(x),\psi(x)$ equivalent in it.