On NSOP₂ theories

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Every nsop2 theory can be categorized as nsop1, highlighting a fundamental relationship between these theory types.
The main result indicates that the structure of nsop2 theories inherently fits within the framework of nsop1.
This work addresses and confirms a question originally posed by Džamonja and Shelah about the classification of theories.
Potential implications might arise in model theory and its foundations based on these dependency structures.

Implication

This analysis shows that all NSOP2 theories belong to the NSOP1 category, suggesting key connections.

Answering a question of Džamonja and Shelah, we show that every {NSOP}₂ theory is {NSOP}₁ .

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Scott Mutchnik (2025) studied this question.

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This analysis shows that all NSOP2 theories belong to the NSOP1 category, suggesting key connections.

Answering a question of Džamonja and Shelah, we show that every {NSOP}₂ theory is {NSOP}₁ .