### 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.

Back to the list of publications