ON ORDERED GROUPS OF MORLEY O-RANK

Verbovskiy V. V.

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

  • Publication Type: Article / Article
  • Volume: 15
  • Publication Date: 2018
  • Doi Number: 10.17377/semi.2018.15.028
  • Title of Journal : SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA
  • Page Numbers: pp.314-320

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.