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Hopfian Groups are Complete co-Analytic

Brian Pinsky

Abstract

We show the set of Hopfian countable groups is a complete co-analytic subset of the standard Borel space of countable groups, resolving a question posed by Simon Thomas (https://doi.org/10.1007/s00153-017-0597-9).

Hopfian Groups are Complete co-Analytic

Abstract

We show the set of Hopfian countable groups is a complete co-analytic subset of the standard Borel space of countable groups, resolving a question posed by Simon Thomas (https://doi.org/10.1007/s00153-017-0597-9).
Paper Structure (4 sections, 5 theorems, 4 equations)

This paper contains 4 sections, 5 theorems, 4 equations.

Table of Contents

  1. Introduction
  2. Generalized wreath products
  3. The proof of Theorem \ref{['T:main']}
  4. Further Questions

Key Result

Theorem 2

$\mathcal{G}_{Hop}$ is a $\Pi_1^1$ complete subset of $\mathcal{G}$.

Theorems & Definitions (9)

  • Definition 1
  • Theorem 2
  • Theorem 3: Friedman-Stanly, fstrees
  • Lemma 4
  • proof
  • Theorem 5: Harrison, harrison
  • Lemma 6
  • proof
  • Definition 7