Keisler's order has infinitely many classes. Malliaris, M. & Shelah, S. Israel Journal of Mathematics.
bibtex   
@article{MiSh:1050,
author = {Malliaris, Maryanthe and Shelah, Saharon},
trueauthor = {Malliaris, Maryanthe and Shelah, Saharon},
fromwhere = {1, IL},
journal = {Israel Journal of Mathematics},
title = {{Keisler's order has infinitely many classes}},
volume = {accepted},
}

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