We show that any rosy CM-trivial theory has weak canonical bases, and CM-triviality in the real sort is equivalent to CM-triviality with geometric elimination of imaginaries. We also show that CM-triviality is equivalent to the modularity in O-minimal theories with elimination of imaginaries.
Ikuo YONEDA. "Some remarks on CM-triviality." J. Math. Soc. Japan 61 (2) 379 - 391, April, 2009. https://doi.org/10.2969/jmsj/06120379