Keisler's order is not simple (and simple theories may not be either). Malliaris, M. & Shelah, S. Annals of Mathematics. arxiv:math/1906.10241
bibtex   
@article{MiSh:1167,
author = {Malliaris, Maryanthe and Shelah, Saharon},
trueauthor = {Malliaris, Maryanthe and Shelah, Saharon},
fromwhere = {1, IL},
journal = {Annals of Mathematics},
note = { arxiv:math/1906.10241 },
title = {{Keisler's order is not simple (and simple theories may not be
 either)}},
}

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