Quasi-o-minimal structures
Küçük Resim Yok
Tarih
2000
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Assn Symbolic Logic Inc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
A structure (M, <....) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal: one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use ii to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1.
Açıklama
Anahtar Kelimeler
Quasi-O-Minimal Theory, O-Minimal Theory, Ordered Group, Theory Of U-Rank 1
Kaynak
Journal of Symbolic Logic
WoS Q Değeri
Q3
Scopus Q Değeri
Q1
Cilt
65
Sayı
3
