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Application of a Tauberian theorem to finite model theory
Authors:Kevin J Compton
Institution:(1) Department of Electrical Engineering and Computer Science, University of Michigan, 48109-1109 Ann Arbor, MI, USA
Abstract:An extension of a Tauberian theorem of Hardy and Littlewood is proved. It is used to show that, for classes of finite models satisfying certain combinatorial and growth properties, Cesàro probabilities (limits of average probabilities over second order sentences) exist. Examples of such classes include the class of unary functions and the class of partial unary functions. It is conjectured that the result holds for the usual notion of asymptotic probability as well as Cesàro probability. Evidence in support of the conjecture is presented.
Keywords:40G05  40G10  03C13
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