Generic Stability Independence and Treeless theories

Itay Kaplan; Nicholas Ramsey; Pierre Simon

Generic Stability Independence and Treeless theories

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arxiv 2305.01296 v2 pith:VN46OHIT submitted 2023-05-02 math.LO

Itay Kaplan , Nicholas Ramsey , Pierre Simon This is my paper

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keywords theoriesindependencetreelessbinaryclassemphgenericstability

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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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Some applications of the real strict order property hierarchy
math.LO 2026-06 unverdicted novelty 7.0 of 10

Real-valued NSOP_r techniques yield that NSOP2subseteq NSOP_r for r>2, an approximate alternative between new real properties and NSOP_n collapse in NTP2, and a sharp SOP2-implies-SOP3 dichotomy for finitely forbidden...

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