Geodesic
On ordered groups of Morley o-rank 1
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 314-320

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Given a cut $s$ in an ordered structure $\mathcal{M}$ we can define a localization of Morley rank—Morley o-rank, replacing each formula in definition of Morley rank with the following partial types: the cut $s$ extended with this formula. We prove in the paper that any ordered group of Morley o-rank 1 with boundedly many definable convex subgroups is weakly o-minimal and construct an example of an ordered group of Morley o-rank 1 and Morley o-degree at most 4.
Keywords: ordered group, weak o-minimality, o-stability, rank. 
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     author = {V. V. Verbovskiy},
     title = {On ordered groups of {Morley} o-rank 1},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {314--320},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a8/}
}
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V. V. Verbovskiy. On ordered groups of Morley o-rank 1. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 314-320. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a8/