The random ordered graph is a semi-retract of the canonically ordered atomless Boolean algebra

TL;DR

This paper proves that the random ordered graph can be embedded as a semi-retract into the canonically ordered atomless Boolean algebra, resolving an open question in the field.

Contribution

It establishes a new semi-retract relationship between the random ordered graph and the ordered Boolean algebra, advancing understanding of their structural connections.

Findings

Confirmed the semi-retract relationship between the random ordered graph and the Boolean algebra.

Answered an open question posed by Bartošová and Scow.

Contributed to the theory of ordered structures and their embeddings.

Abstract

We prove that the random ordered graph is a semi-retract of the canonically ordered atomless Boolean algebra, hereby answering an open question of Barto\v{s}ov\'a and Scow.