On the Elementary Equivalence of Group Factors
Operator Algebras
2025-01-03 v2 Logic
Abstract
We use techniques of distortion systems, introduced by James Hanson to show that any two elementarily equivalent infinite discrete ICC groups give rise to elementarily equivalent group von Neumann algebras. This answers a question raised by Goldbring-Pi (and attributed there to Koichi Oyakawa), in the negative. In a special case, this resolves the model theoretic free factor isomorphism problem.
Keywords
Cite
@article{arxiv.2412.20346,
title = {On the Elementary Equivalence of Group Factors},
author = {Jananan Arulseelan},
journal= {arXiv preprint arXiv:2412.20346},
year = {2025}
}
Comments
Error in main theorem