The Conjugacy Relation on One-sided Subshifts is Non-treeable

TL;DR

This paper investigates the complexity of the conjugacy relation on one-sided subshifts, demonstrating it is non-treeable and non-amenable, thus revealing deep structural properties in symbolic dynamics from a descriptive set theory perspective.

Contribution

It establishes the non-treeability and non-amenability of the conjugacy relation on one-sided subshifts with a binary alphabet, a novel result in the field.

Findings

Conjugacy relation on binary one-sided subshifts is non-treeable.

Conjugacy relation on these subshifts is non-amenable.

Provides new insights into the descriptive set-theoretic complexity of symbolic dynamics.

Abstract

In this paper we study the conjugacy relation on one-sided subshifts in the viewpoint of descriptive set theory. We show the conjugacy relation on one sided subshifts with the alphabet set $\{0,1\}$ is non-treeable and non-amenable.