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Keisler's order is not simple (and simple theories may not be either)
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-09-23 , DOI: 10.1016/j.aim.2021.108036
M. Malliaris 1 , S. Shelah 2, 3
Affiliation  

Solving a decades-old problem we show that Keisler's 1967 order on theories has the maximum number of classes. In fact, it embeds P(ω)/fin. The theories we build are simple unstable with no nontrivial forking, and reflect growth rates of sequences which may be thought of as densities of certain regular pairs, in the sense of Szemerédi's regularity lemma. The proof involves ideas from model theory, set theory, and finite combinatorics.



中文翻译:

凯斯勒的顺序并不简单(简单的理论也可能不简单)

解决一个几十年前的问题,我们表明 Keisler 1967 年的理论顺序具有最大类数。事实上,它嵌入(ω)/. 我们建立的理论是简单的不稳定的,没有非平凡的分叉,并反映了序列的增长率,在 Szemerédi 的正则性引理的意义上,这些可以被认为是某些正则对的密度。证明涉及来自模型论、集合论和有限组合学的思想。

更新日期:2021-09-23
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