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Preprint Number 2404
2404. Isaac Goldbring and Jennifer Pi On the First-Order Free Group Factor Alternative E-mail: Submission date: 14 May 2023 Abstract: We investigate the problem of elementary equivalence of the free group factors, that is, do all free group factors L(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 ∀ ∃-theories of the interpolated free group factors are increasing, and use this to establish that the dichotomy holds on the level of ∀ ∃-theories. We conclude with some observations on related problems. Mathematics Subject Classification: Keywords and phrases: |
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