Abstract
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 ℵ,0-stable theory satisfies I ∞,ℵ0 (T, λ) = 2λ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.
Original language | English |
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Pages (from-to) | 1-46 |
Number of pages | 46 |
Journal | Fundamenta Mathematicae |
Volume | 229 |
Issue number | 1 |
DOIs | |
State | Published - 2015 |
Bibliographical note
Publisher Copyright:© Instytut Matematyczny PAN, 2015.
Keywords
- Borel complete
- Borel reducibility
- ℵ-stable