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Published online by Cambridge University Press: 12 March 2014
We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequences A = { } of finite models, where the universe of
} of finite models, where the universe of  is {1,2, …, n}. and use this framework to strengthen 0-1 laws for logics.
 is {1,2, …, n}. and use this framework to strengthen 0-1 laws for logics.