Tame Expansions of omega-Stable Theories and Definable Groups

Goral H.

NOTRE DAME JOURNAL OF FORMAL LOGIC, vol.60, no.2, pp.161-194, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1215/00294527-2019-0003
  • Journal Name: NOTRE DAME JOURNAL OF FORMAL LOGIC
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.161-194
  • Keywords: model theory, stability, Mann property, PAIRS
  • Dokuz Eylül University Affiliated: Yes

Abstract

We study groups definable in tame expansions of omega-stable theories. Assuming several tameness conditions, we obtain structural theorems for groups definable and interpretable in these expansions. As our main example, by characterizing independence in the pair (K, G), where K is an algebraically closed field and G is a multiplicative subgroup of K-x with the Mann property, we show that the pair (K, G) satisfies the assumptions. In particular, this provides a characterization of definable and interpretable groups in (K, G) in terms of algebraic groups in K and interpretable groups in G. Furthermore, we compute the Morley rank and the U-rank in. (K, G) and both ranks agree.