Abstract
We prove that the class of 231-avoiding permutations satisfies a logical limit law, i.e. that for any first-order sentence [PSI], in the language of two total orders, the probability [p.sub.n,[PSI]] that a uniform random 231-avoiding permutation of size n satisfies [PSI] admits a limit as n is large. Moreover, we establish two further results about the behavior and value of [p.sub.n,[PSI]]: (i) it is either bounded away from 0, or decays exponentially fast; (ii) the set of possible limits is dense in [0,1]. Our tools come mainly from analytic combinatorics and singularity analysis.