# Sh:1016

- Laskowski, M. C., & Shelah, S. (2015).
*Borel completeness of some \aleph_0-stable theories*. Fund. Math.,**229**(1), 1–46. arXiv: 1211.0558 DOI: 10.4064/fm229-1-1 MR: 3312114 -
Abstract:

We study \aleph_0-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 \lambda-Borel completeness and prove that such theories are \lambda-Borel complete. Using this, we conclude that an \aleph_0-stable theory satisfies I_{\infty, \aleph_0}(T, \lambda) = 2^\lambda for all cardinals \lambda if and only if T either has eni-DOP or is eni-deep. - published version (46p)

Bib entry

@article{Sh:1016, author = {Laskowski, Michael Chris and Shelah, Saharon}, title = {{Borel completeness of some $\aleph_0$-stable theories}}, journal = {Fund. Math.}, fjournal = {Fundamenta Mathematicae}, volume = {229}, number = {1}, year = {2015}, pages = {1--46}, issn = {0016-2736}, doi = {10.4064/fm229-1-1}, mrclass = {03C45 (03E15)}, mrnumber = {3312114}, mrreviewer = {John Goodrick}, doi = {10.4064/fm229-1-1}, note = {\href{https://arxiv.org/abs/1211.0558}{arXiv: 1211.0558}}, arxiv_number = {1211.0558} }