  Let $\alpha \in (0,1)_{\mathbb{R}}$ be irrational and $G_n =
G_{n,1/n^\alpha}$ be the random graph with edge probability $1/n^\alpha$; we
know that it satisfies the 0-1 law for first order logic. We deal with the
failure of the 0-1 law for stronger logics: $\mathbb{L}_{\infty,k},k$ large
enough and the inductive logic.
