On a conjecture for $\aleph_0$-bounded groups

TL;DR

This paper demonstrates the relative consistency of a generalized Borel Conjecture with the failure of the classical Borel Conjecture, assuming a strongly inaccessible cardinal.

Contribution

It establishes a consistency result linking the generalized and classical Borel Conjectures within set theory.

Findings

The generalized Borel Conjecture can hold while the classical one fails.

Consistency is shown relative to a strongly inaccessible cardinal.

The result advances understanding of the independence of Borel Conjectures.

Abstract

We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [8] holds while the classical Borel Conjecture fails.