Independence in randomizations

Uri Andrews; Isaac Goldbring; H. Jerome Keisler

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arXiv · 1610.09270

Independence in randomizations

Uri Andrews·Isaac Goldbring·H. Jerome Keisler

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Abstract

The randomization of a complete first order theory $T$ is the complete continuous theory $T^R$ with two sorts, a sort for random elements of models of $T$, and a sort for events in an underlying atomless probability space. We study independence relations and related ternary relations on the randomization of $T$. We show that if $T$ has the exchange property and $\operatorname{acl}=\operatorname{dcl}$, then $T^R$ has a strict independence relation in the home sort, and hence is real rosy. In particular, if $T$ is o-minimal, then $T^R$ is real rosy.

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BibTeX RIS

Uri Andrews, Isaac Goldbring, H. Jerome Keisler. 2016-10-28. Independence in randomizations. https://arxiv.org/abs/1610.09270

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