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arXiv · 0901.1584

On theories of random variables

Itaï Ben Yaacov
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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: i) The randomisation of a stable structure is stable. ii) 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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Itaï Ben Yaacov. 2011-11-08. On theories of random variables. https://doi.org/10.1007/s11856-012-0155-4

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