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Preprint Number 159

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159. Itaï Ben Yaacov
On theories of random variables
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Submission date: 24 January 2009.

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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