# On the automorphism group of the universal homogeneous meet-tree

## TL;DR

This paper investigates the automorphism group of the countable universal homogeneous meet-tree, demonstrating the existence of a generic automorphism but the absence of a generic pair of automorphisms.

## Contribution

It establishes the existence of a generic automorphism in the structure and proves that no generic pair exists, advancing understanding of automorphism groups in homogeneous structures.

## Key findings

- Existence of a generic automorphism in the meet-tree.
- Non-existence of a generic pair of automorphisms.
- Insights into the automorphism group's structure.

## Abstract

We show that the countable universal homogeneous meet-tree has a generic automorphism, but it does not have a generic pair of automorphisms.