In Erdos-Renyi random graph $G(n,p(n))$; set $p(n)= (\frac{ln n}{n})^2$. We know that already Spencer and Shelah have proved that zero-one law doesn't hold for $p(n)= \frac{ln n}{n}$. Now the question is that will it satisfy for any exponent of $\frac{ln n}{n}$? Or again will not satisfy? (or may be it will satisfy for some exponents and for some of them not?)
I will appreciate your comments and possible solutions or any ideas for to start and prove it!
Thanks a lot!