Borel completeness of some $aleph_0$-stable theories

by Laskowski and Shelah. [LwSh:1016]
Fundamenta Math, 2015
We study aleph_0-stable theories, and prove that if T either has eni-DOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of lambda-Borel completeness and prove that such theories are lambda-Borel complete. Using this, we conclude that an aleph_0-stable theory satisfies I_{infty, aleph_0}(T, lambda) = 2^lambda for all cardinals lambda if and only if T either has eni-DOP or is eni-deep.


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