On theories of random variables
Résumé
We study theories of spaces of random variables: first, we consider random variables with values in the interval $[0,1]$, then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: \begin{enumerate} \item The randomisation of a stable structure is stable. \item The randomisation of a simple unstable structure is not simple. \end{enumerate} We also prove that in the randomised structure, every type is a Lascar type.
Domaines
Logique [math.LO]
Origine : Fichiers produits par l'(les) auteur(s)