Probabilities of Sentences about Very Sparse Random Graphs
James Francis Lynch · Random Structures and Algorithms · 1992
Abstract We consider 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. We prove that for every first‐order sentence, the probability that the sentence is true for the random graph has an asymptotic limit.