Geodesic
Cayley's theorem for ordered groups: $o$-minimality
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 278-281 
Bektur Baizhanov; John Baldwin; Viktor Verbiovskiy. Cayley's theorem for ordered groups: $o$-minimality. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 278-281. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a15/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It has long been known [1] that any group could be represented in a strongly minimal theory by just writing down the relations of the group as unary functions. We show the same process works for ordered groups and yields an $o$-minimal group.

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[2] D. J. S. Robinson, A course in the theory of Groups, Springer-Verlag, New York, Heidelberg, Berlin, 1982 | MR

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[4] A. Pillay and Ch. Steinhorn, “Definable sets in ordered structures I”, Transactions of the American Mathematical Society, 295 (1986), 565–592 | DOI | MR | Zbl

[5] D. Marker and Ch. Steinhorn, “Definable types in $o$-minimal theories”, The Journal of Symbolic Logic, 59 (1994), 155–194 | DOI | MR