Forum of Mathematics, Sigma (Jan 2024)

Generic Stability Independence and Treeless Theories

  • Itay Kaplan,
  • Nicholas Ramsey,
  • Pierre Simon

DOI
https://doi.org/10.1017/fms.2024.35
Journal volume & issue
Vol. 12

Abstract

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We initiate a systematic study of 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.

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