I don't know how I can show that $0-1$ law for $G(n,n,p)$, i.e.
every first order sentence either a.a.s. true on $G(n,n,p)$ or a.a.s. false on $G(n,n,p)$. Here, we assume that $p$ is constant (does not depend on $n$).
Here, Let $G(n,n,p)$ be binomial subgraph of complete bipartite graph $K_{n,n}$ (we have two parts. each of size $n$, every edge between two vertices from different parts appears in the random graph with probability $p$, and there are no edges between vertices of the same part).
"Could you please hint me about that of introduce me any papers about this or "Zero-One Laws" for $G(n,p)$?