Abstract
We study theorems of ordered groups from the perspective of reverse mathematics. We show that $\mathit{RCA}_0$ suffices to prove Hölder's Theorem and give equivalences of both $\mathit{WKL}_0$ (the orderability of torsion free nilpotent groups and direct products, the classical semigroup conditions for orderability) and $\mathit{ACA}_0$ (the existence of induced partial orders in quotient groups, the existence of the center, and the existence of the strong divisible closure).
Citation
Reed Solomon. "Reverse Mathematics and Fully Ordered Groups." Notre Dame J. Formal Logic 39 (2) 157 - 189, Spring 1998. https://doi.org/10.1305/ndjfl/1039293061
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