# Examples of weak amalgamation classes

## TL;DR

This paper provides examples of hereditary classes of finite structures that satisfy some amalgamation properties but fail others, illustrating the nuanced relationships between these properties in model theory.

## Contribution

It introduces multiple examples of classes with specific amalgamation property combinations, including a continuum-sized family and a countably categorical example.

## Key findings

- Several classes satisfy joint embedding and weak amalgamation but not cofinal amalgamation.
- Includes a continuum-sized family of graph classes demonstrating these properties.
- Provides an example with a countably categorical generic limit.

## Abstract

We present several examples of hereditary classes of finite structures satisfying the joint embedding property and the weak amalgamation property, but failing the cofinal amalgamation property. These include a continuum-sized family of classes of finite undirected graphs, as well as an example due to Pouzet with countably categorical generic limit.