With identity I mean that there is an equivalent statement. With logicall I mean that this statement deals with EF-games.
I want to prove that
A function $p(n)\in [0,1]$ satisfies the Zero one laws iff for every first order logical statement $A$ over the signature for graphs $\lim_{n\rightarrow\infty}Pr[((G,n,p(n)))\models A]=1 \vee 0$
I want to show now that
A function satisfies the zero one laws iff for every $t,G(n,p(n)),H(m,p(m)):\lim_{m,n\rightarrow\infty}Pr[\texttt{Duplicator wins EHR[G,n,p(n),H(m,p(m)),t]}]=1$
$\Leftarrow$ is proved in the book (proof Theorem 10.7.4). How can I prove the other direction?
