Submission date: 2 May 2023

Abstract:

We initiate a systematic study of \emph{generic stability independence} and introduce the class of 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.

Mathematics Subject Classification:

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Full text arXiv 2305.01296: pdf, ps.