Borel completeness of some ℵ0stable theories

Michael C. Laskowski; Saharon Shelah

doi:10.4064/fm229-1-1

Borel completeness of some ℵ₀stable theories

Michael C. Laskowski
, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

9 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) = 2^λ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.

Original language	English
Pages (from-to)	1-46
Number of pages	46
Journal	Fundamenta Mathematicae
Volume	229
Issue number	1
DOIs	https://doi.org/10.4064/fm229-1-1
State	Published - 2015

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2015.

Keywords

Borel complete
Borel reducibility
ℵ-stable

Access to Document

10.4064/fm229-1-1

Cite this

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