The Wallace problem in ZFC

Source: arxiv:2608.17317, doi:10.48550/arXiv.2608.17317, url:https://github.com/vo-rodrigues/wallace-problem-zfc-paper Authors: Juliane Trianon Fraga, Vinicius de Oliveira Rodrigues Status: verified Main declarations: Wallace.commutativeTychonoffWallaceCounterexampleExists Tags: wallace-problem, topological-groups, set-theoretic-topology MSC: 22A05, 54D30, 20K20

Countably compact groups and the Wallace counterexample

This library proves the paper's main theorem for every torsion-free Abelian group of cardinality continuum. It also exposes the free, rational, real, and Baer--Specker specializations. The nonnegative cone in the free Abelian group gives a commutative Tychonoff countably compact cancellative topological additive monoid which is not a group. The internal Section 10 propositions on large closures and suitable sets are included as well.

The public entry point exposes the three principal statements from the paper.