ON ORDERED GROUPS OF MORLEY O-RANK
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, cilt.15, ss.314-320, 2018 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 15
- Basım Tarihi: 2018
- Doi Numarası: 10.17377/semi.2018.15.028
- Dergi Adı: SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.314-320
- Süleyman Demirel Üniversitesi Adresli: Hayır
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.