A normal form theorem for lω 1p, with applications

Journal of Symbolic Logic 47 (3):605 - 624 (1982)
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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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Citations of this work

Probability logic with conditional expectation.Sergio Fajardo - 1985 - Annals of Pure and Applied Logic 28 (2):137-161.
Confirming Inexact Generalizations.Ernest W. Adams - 1988 - PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988 (1):10-16.

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Probability logic.Douglas N. Hoover - 1978 - Annals of Mathematical Logic 14 (3):287.

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