Year: 2023
Type: preprint
Abstract: We investigate the problem of elementary equivalence of the free group factors, that is, do all free group factors $L(\mathbb{F}_n)$ share a common first-order theory? We establish a trichotomy of possibilities for their common first-order fundamental group, as well as several possible avenues for establishing a dichotomy in direct analog to the free group factor alternative of Dykema and Radulescu. We also show that the $\forall \exists$-theories of the interpolated free group factors are increasing, and use this to establish that the dichotomy holds on the level of $\forall \exists$-theories. We conclude with some observations on related problems.
Source: arXiv (Cornell University)
Authors: Goldbring, Isaac, Pi, Jennifer
Institutions: University of California, Irvine, Irvine University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4376653578