Consider the binomial random graph model $G(n,p)$ with $0<p<1$. We say that $G(n,p)$ satisfies the Zero-One law if for every first order property $Q$ one has $\lim\limits_{n \rightarrow \infty} Pr(G(n,p)~ has~ property~ Q) \in \{ 0, 1 \}$. And as it has been proved by Shelah and Spencer in 1988, it doesn't satisfy the Zero-One law if $p(n)$ equals to one of the functions $n^{-1 - \frac{1}{k}}$, $n^{-1}$, $n^{-1} ln n$ and $n^{- \alpha}$ for rational $0< \alpha < 1$.

Now one of the interesting questions which seems common here to ask is that if we take $p(n) = \sqrt{n^{-1} ln n}$, will zero-one law still not be satisfied? or will satisfy? and why?

Thanks!