Generic Stability Independence and Treeless Theories

Itay Kaplan; Nicholas Ramsey; Pierre Simon

doi:10.1017/fms.2024.35

Generic Stability Independence and Treeless Theories

Itay Kaplan
, Nicholas Ramsey
, Pierre Simon

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

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 NSOP₃ theory is simple.

Original language	English
Article number	e49
Journal	Forum of Mathematics, Sigma
Volume	12
DOIs	https://doi.org/10.1017/fms.2024.35
State	Published - 8 Apr 2024

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1017/fms.2024.35

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AB - 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.

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DO - 10.1017/fms.2024.35

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VL - 12

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e49

ER -

Generic Stability Independence and Treeless Theories

Abstract

ASJC Scopus subject areas

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