# Amalgamation of types in pseudo-algebraically closed fields and applications

## TL;DR

This paper explores the structure of unbounded PAC fields, demonstrating an amalgamation result for types over algebraically closed sets, and discusses applications including properties of omega-free PAC fields and imaginaries in PAC fields.

## Contribution

It introduces a new amalgamation theorem for types in unbounded PAC fields and applies it to analyze properties like NSOP3 and imaginaries.

## Key findings

- Omega-free PAC fields have property NSOP3
- Description of imaginaries in PAC fields
- Amalgamation result for types over algebraically closed sets

## Abstract

This paper studies unbounded PAC fields and shows an amalgamation result for types over algebraically closed sets. It discusses various applications, for instance that omega-free PAC fields have the property NSOP3. It also contains a description of imaginaries in PAC fields.