A preservation theorem for theories without the tree property of the first kind

TL;DR

This paper proves that the NTP$_1$ property is preserved in certain related theories and provides examples of non-simple geometric NTP$_1$ theories, advancing understanding of model-theoretic properties.

Contribution

It establishes preservation results for NTP$_1$ in lovely pairs and H-structures, and introduces new examples of non-simple geometric NTP$_1$ theories.

Findings

NTP$_1$ is inherited by theories of lovely pairs and H-structures.

Provided examples of non-simple geometric NTP$_1$ theories.

Enhanced understanding of the structure of NTP$_1$ theories.

Abstract

We prove that the NTP$_1$ property of a geometric theory $T$ is inherited by theories of lovely pairs and $H$-structures associated to $T$. We also provide a class of examples of nonsimple geometric NTP$_1$ theories.