Independence in randomizations

2016/10/28 by Uri Andrews, Andrews, Uri, Isaac Goldbring +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algorithms and Data Compression #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1610.09270

openalex publication_date 2016/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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 acl=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.

Related

• Independence relations in randomizations
• Algebraic Independence Relations in Randomizations
• Definable closure in randomizations
• Simple Models of Randomization and Preservation Theorems
• Axiomatic Theory of Independence Relations in Model Theory