A Normal Form Theorem for $L_{\omega 1p}$, with Applications

Hoover, Douglas N.

J. Symbolic Logic, Tome 47 (1982) no. 1, p. 605-624 / Harvested from Project Euclid

Résumé

We show that every formula of $L_{\omega 1p}$ 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 $L_{\omega 1p}$.

Publié le : 1982-09-14
Classification:

@article{1183741089,
     author = {Hoover, Douglas N.},
     title = {A Normal Form Theorem for $L\_{\omega 1p}$, with Applications},
     journal = {J. Symbolic Logic},
     volume = {47},
     number = {1},
     year = {1982},
     pages = { 605-624},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183741089}
}

Hoover, Douglas N. A Normal Form Theorem for $L_{\omega 1p}$, with Applications. J. Symbolic Logic, Tome 47 (1982) no. 1, pp.  605-624. http://gdmltest.u-ga.fr/item/1183741089/