Generic Stability Independence and Treeless Theories
Itay Kaplan, Nicholas Ramsey, Pierre Simon · Forum of Mathematics Sigma · 2024
Abstract 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.