Definable closure in randomizations

2013/04/29 by Uri Andrews, Andrews, Uri, Isaac Goldbring +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO

paper · pdf · doi:10.48550/arxiv.1304.7797

19 pages

arxiv created 2013/04/29 · openalex publication_date 2013/04/29 · arxiv updated 2013/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 probability space. We give necessary and sufficient conditions for an element to be definable over a set of parameters in a model of T^R.

Related

• Independence relations in randomizations
• Independence in randomizations
• Simple Models of Randomization and Preservation Theorems
• Algebraic Independence Relations in Randomizations
• Metric Structures and Probabilistic Computation