Groups from walks on countable ordinals

Abstract

This paper deals with topological groups constructed from characteristics of walks on countable ordinals. We introduce two groups, constructed from ρ<inf>1</inf> and ρ<inf>3</inf>, and show they are both Fréchet, non-metrizable and that the topological group constructed from ρ<inf>1</inf> has the maximal Tukey type among topological groups of character ω<inf>1</inf>. We also consider the group associated with ρ<inf>2</inf> introduced in [12] and show that under some set-theoretic assumptions the group does not have the maximal Tukey type.