ON ORDERED GROUPS OF MORLEY O-RANK

Verbovskiy V. V.

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, cilt.15, ss.314-320, 2018 (ESCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 15
  • Basım Tarihi: 2018
  • Doi Numarası: 10.17377/semi.2018.15.028
  • Dergi Adı: SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA
  • Sayfa Sayıları: ss.314-320

Özet

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.