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

Ruiwen Li

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.

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

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 is non-treeable and non-amenable.
Paper Structure (3 sections, 7 theorems, 19 equations)

This paper contains 3 sections, 7 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of the Main Theorem

Key Result

Theorem 1.2

The conjugacy relation on transitive one-sided subshifts with the alphabet set $\{0,1\}$ is a non-treeable and non-amenable countable Borel equivalence relation.

Theorems & Definitions (15)

  • Theorem 1.2
  • Theorem 2.1
  • Definition 3.1: paper
  • Definition 3.2: paper
  • Theorem 3.3: paper
  • Lemma 3.4
  • proof
  • Theorem 3.5
  • proof
  • proof
  • ...and 5 more