On theories of random variables |
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Authors: | Itaï Ben Yaacov |
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Affiliation: | 1155. Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard — Lyon 1, 43 boulevard du 11 novembre 1918, 69622, Villeurbanne Cedex, France
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Abstract: | 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: - The randomisation of a stable structure is stable.
- The randomisation of a simple unstable structure is not simple.
We also prove that in the randomised structure, every type is a Lascar type. |
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