Expansions of the real field by discrete subgroups of Gln(C)

Philipp Hieronymi; Erik Walsberg; Samantha Xu

doi:10.1090/proc/15382

Expansions of the real field by discrete subgroups of Gl_n(C)

Philipp Hieronymi, Erik Walsberg, Samantha Xu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let Γ be an infinite discrete subgroup of Gl_n(C). Then either (R, <, +, ·, Γ) is interdefinable with (R, <, +, ·, λ^Z) for some real number λ, or (R, <, +, ·, Γ) defines the set of integers. When Γ is not virtually abelian, the second case holds.

Original language	English (US)
Pages (from-to)	2221-2233
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	5
DOIs	https://doi.org/10.1090/proc/15382
State	Published - May 2021

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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Cite this

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abstract = "Let Γ be an infinite discrete subgroup of Gln(C). Then either (R, <, +, ·, Γ) is interdefinable with (R, <, +, ·, λZ) for some real number λ, or (R, <, +, ·, Γ) defines the set of integers. When Γ is not virtually abelian, the second case holds.",

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