Borel completeness of some ℵ₀-stable theories

• Autorzy: Michael C. Laskowski , Saharon Shelah
• Języki publikacji: 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.

Kategorie tematyczne

• 03E15: Descriptive set theory
• 03C45: Classification theory, stability and related concepts

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 229
• Numer: 1
• Strony: 1-46

Daty

wydano

2015

Twórcy

autor

Michael C. Laskowski

• Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.

autor

Saharon Shelah

• 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.

Identyfikatory

DOI

10.4064/fm229-1-1