Universality of group embeddability

Abstract

Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the isometric embeddability between separable groups with a bounded bi-invariant complete metric are all invariantly universal analytic quasi-orders. This strengthens some results from [Wil14] and [FLR09].

Minor corrections. 15 pages, submitted

References in corpus (2)

• Invariantly universal analytic quasi-orders
• Universal countable Borel quasi-orders

Cited by in corpus (2)

• Uncountable structures are not classifiable up to bi-embeddability
• Classification problems from the descriptive set theoretical perspective