# Topological and almost Borel Universality for systems with the weak specification property

## TL;DR

This paper demonstrates that systems with certain specification properties can universally embed aperiodic subshifts with lower entropy, highlighting their broad topological and Borel universality.

## Contribution

It establishes the universality of systems with specification properties for embedding aperiodic subshifts, advancing understanding of their structural complexity.

## Key findings

- Systems with specification properties are topologically universal.
- Such systems can embed any aperiodic subshift with lower entropy.
- They are also almost Borel universal.

## Abstract

We show that systems with some specification properties are topologically or almost Borel universal, in the sense that any aperiodic subshift with lower entropy may be topologically or almost Borel embedded.