Notre Dame Journal of Formal Logic

Reverse Mathematics and Fully Ordered Groups

Reed Solomon


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).

Article information

Notre Dame J. Formal Logic, Volume 39, Number 2 (1998), 157-189.

First available in Project Euclid: 7 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]
Secondary: 03F35: Second- and higher-order arithmetic and fragments [See also 03B30]


Solomon, Reed. Reverse Mathematics and Fully Ordered Groups. Notre Dame J. Formal Logic 39 (1998), no. 2, 157--189. doi:10.1305/ndjfl/1039293061.

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