Merges of Smooth Classes and Their Properties

TL;DR

This paper investigates the merging of Fraïssé-like classes with generic limits, exploring their properties, connections to structural Ramsey theory, and the Hrushovski property, to understand how such merges can be constructed and characterized.

Contribution

It introduces a framework for merging Fraïssé-like classes with generic limits and analyzes their properties and connections to key concepts in model theory.

Findings

Merges of Fraïssé-like classes can preserve generic limits under certain conditions.

Connections between merges and the structural Ramsey property are established.

The study reveals how merges relate to the Hrushovski property (EPPA).

Abstract

Given two Fra\"iss\'e-like classes with generic limits, we ask whether we can merge the two classes into one class with a generic limit. We study the properties of these merges and their generics, as well as their connections to structural Ramsey theory and the Hrushovski property (EPPA).