Abstract: 

The class of [0,1]-valued random variables on atomless probability spaces is an elementary class in  continuous logic. The theory of this class is denoted by ARV. ARV is complete, separably categorical, omega-stable, and admits quantifier elimination. During this talk, we will characterize saturated models of ARV, and give explicit formulas between types. Finally, we will discuss type spaces of ARV and Wasserstein spaces.