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A normal form theorem for Lω1p, with applications

Published online by Cambridge University Press:  12 March 2014

Douglas N. Hoover
Douglas N. Hoover*
Affiliation:
Yale University, New Haven, Connecticut 06520
*
Queen's University, Kingston, Ontario K7L 3N6, Canada
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Abstract

We show that every formula of Lω1P 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 Lω1P.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 3 , September 1982 , pp. 605 - 624
Copyright
Copyright © Association for Symbolic Logic 1982

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References

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