Probabilities of sentences about very sparse random graphs

The author considers random graphs with edge probability βn^-α, where n is the number of vertices of the graph, β>0 is fixed, and α=1 or α=( l+1)/l for some fixed positive integer l. It is proved that, for every first-order sentence, the probability that the sentence is true for the random graph has an asymptotic limit. Also, there is an effective procedure for generating the value of the limit in closed form