ON ORDERED GROUPS OF MORLEY O-RANK


Verbovskiy V. V.

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, vol.15, pp.314-320, 2018 (ESCI) identifier identifier

Abstract

Given a cut s in an ordered structure 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.