Ample Pairs

TL;DR

This paper proves that the ample degree of a stable trivial forking theory remains unchanged when extended to belles paires or H-structures of rank 1, highlighting stability properties in model theory.

Contribution

It establishes the preservation of ample degree in belles paires and H-structures for trivial stable theories, extending understanding of stability in these structures.

Findings

Ample degree is preserved in belles paires.

Results apply to H-structures of trivial rank 1.

Enhances understanding of stability in model-theoretic structures.

Abstract

We show that the ample degree of a stable theory with trivial forking is preserved when we consider the corresponding theory of belles paires, if it exists. This result also applies to the theory of $H$-structures of a trivial theory of rank $1$.