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Reverse mathematics and fully ordered groups. (English) Zbl 0973.03076
This article is a detailed presentation of some of the author’s work in the reverse mathematics of ordered groups, including proofs of many of the results listed in his survey article [Bull. Symb. Log. 5, No. 1, 45-58 (1999; Zbl 0922.03078)]. Theorems pertaining to quotient groups, product groups, and semigroup conditions for orderability are analyzed, and a proof of Hölder’s theorem is carried out in RCA$$_0$$. Related results can also be found in the author’s paper [J. Symb. Log. 66, No. 1, 192-206 (2001; Zbl 0981.03060)].

MSC:
 03F35 Second- and higher-order arithmetic and fragments 06F15 Ordered groups 03B30 Foundations of classical theories (including reverse mathematics)
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References:
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