, Volume 194, Issue 2, pp 957-1012
Date: 07 Aug 2013

On theories of random variables

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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:

  1. The randomisation of a stable structure is stable.

  2. The randomisation of a simple unstable structure is not simple.

We also prove that in the randomised structure, every type is a Lascar type.

The author wishes to thank the referee for many helpful remarks regarding the structure of the articles and references.
Research supported by ANR chaire d’excellence junior THEMODMET (ANR-06-CEXC-007) and by Marie Curie research network ModNet