TL;DR
This paper proves that all NSOP$_2$ theories are also NSOP$_1$, answering a question posed by Džamonja and Shelah and clarifying the relationship between these classes of theories.
Contribution
It establishes that the class of NSOP$_2$ theories is contained within NSOP$_1$, providing a significant insight into the hierarchy of model-theoretic properties.
Findings
Every NSOP$_2$ theory is NSOP$_1$.
The result answers an open question in model theory.
Clarifies the relationship between NSOP$_2$ and NSOP$_1$ classes.
Abstract
Answering a question of D\v{z}amonja and Shelah, we show that every NSOP theory is NSOP.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Holomorphic and Operator Theory