A normal form theorem for lω 1p, with applications

Journal of Symbolic Logic 47 (3):605 - 624 (1982)
Abstract
We show that every formula of L ω 1p is equivalent to one which is a propositional combination of formulas with only one quantifier. It follows that the complete theory of a probability model is determined by the distribution of a family of random variables induced by the model. We characterize the class of distribution which can arise in such a way. We use these results together with a form of de Finetti's theorem to prove an almost sure interpolation theorem for L ω 1p
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Sergio Fajardo (1985). Probability Logic with Conditional Expectation. Annals of Pure and Applied Logic 28 (2):137-161.
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