Transfer of generalized amalgamation in simple theories

TL;DR

This paper develops an abstract framework for transferring generalized amalgamation properties between simple theories and applies it to specific classes like lovely pairs and bounded PAC structures, demonstrating broad applicability.

Contribution

It introduces a novel abstract framework for transferring generalized amalgamation across simple theories, including applications to lovely pairs and bounded PAC structures.

Findings

Bounded pseudo-algebraically closed fields have generalized amalgamation.

The framework applies regardless of the imperfection degree.

The approach extends amalgamation transfer to new classes of theories.

Abstract

We give an abstract framework to transfer generalized amalgamation from a simple theory to another, and we apply it to theories of lovely pairs and of bounded PAC structures. We show in particular that bounded pseudo-algebraically closed fields have generalized amalgamation, regardless of their imperfection degree.