As proved, the first-order sentences provable from the extension axioms and modeled by the Rado graph are exactly the sentences true for almost all random finite graphs. This means that if one chooses an -vertex graph uniformly at random among all graphs on labeled vertices, then the probability that such a sentence will be true for the chosen graph approaches one in the limit as approaches infinity. Symmetrically, the sentences that are not modeled by the Rado graph are false for almost all random finite graphs. It follows that every first-order sentence is either almost always true or almost always false for random finite graphs, and these two possibilities can be distinguished by determining whether the Rado graph models the sentence. Fagin's proof uses the compactness theorem, Based on this equivalence, the theory of sentences modeled by the Rado graph has been called "the theory of the random graph" or "the almost sure theory of graphs".