Book Description
Abstract: "We investigate asymptotic probabilities of properties expressible in the infinitary logic [formula] on finite structures. Sentences in this logic may have arbitrary disjunctions and conjunctions, but they involve only a finite number of distinct variables. We show that the 0-1 law holds for [formula], i.e., the asymptotic probability of every sentence in this logic exists and is equal to either 0 or 1. This result subsumes earlier work on asymptotic probabilities for various fixpoint logics and reveals the boundary of 0-1 laws for infinitary logics."