# Probabilities on finite models

@article{Fagin1976ProbabilitiesOF, title={Probabilities on finite models}, author={Ronald Fagin}, journal={Journal of Symbolic Logic}, year={1976}, volume={41}, pages={50 - 58} }

Let be a finite set of (nonlogical) predicate symbols. By an -structure, we mean a relational structure appropriate for . Let be the set of all -structures with universe {1, …, n}. For each first-order -sentence σ (with equality), let μn(σ) be the fraction of members of for which σ is true. We show that μn(σ) always converges to 0 or 1 as n → ∞, and that the rate of convergence is geometrically fast. In fact, if T is a certain complete, consistent set of first-order -sentences introduced by H…

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