# Countably compact groups and sequential order

**Authors:** Dmitri Shakhmatov, Alexander Shibakov

arXiv: 1903.08041 · 2019-03-20

## TL;DR

None

## Contribution

None

## Abstract

We use $\diamondsuit$ to construct, for every $\alpha\leq\omega_1$ a sequential countably compact topological group of sequential order $\alpha$. This establishes the independence of the existence of sequential countably compact non Fr\'echet groups from the usual axioms of ZFC and answers several questions of D.~Shakhmatov.

## Full text

_Full body text omitted from this summary view._ Fetch the complete paper as Markdown: https://tomesphere.com/paper/1903.08041/full.md

## References

24 references — full list in the complete paper: https://tomesphere.com/paper/1903.08041/full.md

---
Source: https://tomesphere.com/paper/1903.08041