Borel completeness of some ℵ0stable theories

Michael C. Laskowski, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 languageEnglish
Pages (from-to)1-46
Number of pages46
JournalFundamenta Mathematicae
Volume229
Issue number1
DOIs
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2015.

Keywords

  • Borel complete
  • Borel reducibility
  • ℵ-stable

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