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arXiv · 2305.01296

Generic Stability Independence and Treeless theories

Itay Kaplan·Nicholas Ramsey·Pierre Simon
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Abstract

We initiate a systematic study of \emph{generic stability independence} and introduce the class of \emph{treeless theories} in which this notion of independence is particularly well-behaved. We show that the class of treeless theories contains both binary theories and stable theories and give several applications of the theory of independence for treeless theories. As a corollary, we show that every binary NSOP$_{3}$ theory is simple.

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Itay Kaplan, Nicholas Ramsey, Pierre Simon. 2023-05-02. Generic Stability Independence and Treeless theories. https://arxiv.org/abs/2305.01296

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