Interpretation and bi-interpretation offer a novel approach to studying all structures elementarily equivalent to a given one. We use this approach to describe and study non-standard models of the ring of polynomials, Laurent polynomials, and the group ring of a free group.
In the presence of interpretation but not bi-interpretation, this approach produces a family of structures elementarily equivalent to a given one. We exploit this to introduce non-standard models of a free group. As time permits, we discuss their main properties.
The talk is based on joint work with Alexei Miasnikov.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
