First order properties of random posets

Let =(n,p) be a binary relation on the set n]={1, 2, ..., n} such that (i,i) for every i and (i,j) with probability p, independently for each pair i,j n], where i<j. Define as the transitive closure of and denote poset (n], ) by R(n, p). We show that for any constant p probability of each first order property of R(n, p) converges as n .