Year: 2021
Type: preprint
Abstract: In this paper we initiate a study of first-order rich groups, i.e., groups where the first-order logic has the same power as the weak second order logic. Surprisingly, there are quite a lot of finitely generated rich groups, they are somewhere in between hyperbolic and nilpotent groups (these ones are not rich). We provide some methods to prove that groups (and other structures) are rich and describe some of their properties. As corollaries we look at Malcev's problems in various groups.
Source: arXiv (Cornell University)
Institution: Stevens Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: City University of New York
Award: G66941040
OpenAlex ID: W4301180975