Generic Stability Independence and Treeless Theories

Itay Kaplan, Nicholas Ramsey*, Pierre Simon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 NSOP3 theory is simple.

Original languageAmerican English
Article numbere49
JournalForum of Mathematics, Sigma
StatePublished - 8 Apr 2024

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