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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2015 | 229 | 1 | 1-46

## Borel completeness of some ℵ₀-stable theories

EN

### Abstrakty

EN
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 $I_{∞,ℵ₀}(T,λ) = 2^{λ}$ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.

1-46

wydano
2015

### Twórcy

autor
• Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.
autor
• Department of Mathematics, The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904, Israel
• Department of Mathematics, Hill Center, Busch Campus, Rutgers, the State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-9019, U.S.A.