We work in the context of ω-stable theories. We obtain a natural, algebraic equivalent of ENI-NDOP and discuss recent joint proofs with Shelah that if an ω-stable theory has either ENI-DOP or is ENI-NDOP and is ENI-deep, then the set of models of T with universe ω is Borel complete.
"An Old Friend Revisited: Countable Models of ω-Stable Theories." Notre Dame J. Formal Logic 48 (1) 133 - 141, 2007. https://doi.org/10.1305/ndjfl/1172787550