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Borel completeness of some ℵ₀-stable theories

Michael C. Laskowski, Saharon Shelah (2015)

Fundamenta Mathematicae

We study ℵ₀-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 λ-Borel completeness and prove that such theories are λ-Borel complete. Using this, we conclude that an ℵ₀-stable theory satisfies I , ( T , λ ) = 2 λ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.

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