Submission date: 3 July 2009. Revised: 12 May 2010.

Abstract:

An ordered structure M is called o-k-stable if for any subset A with |A| at most k and for any cut in M there are at most k 1-types over A which are consistent with the cut. It is proved in the paper that an ordered o-stable group is abelian. Also there were investigated definable subsets and unary functions of o-stable groups.

Version of 12 May 2010: corrected some typos and inexactness in the proof of Lemma 1.7, Lemma 1.10, Theorem 3.12 (in old numeration).

Mathematics Subject Classification: 03C45, 03C64

Keywords and phrases: o-minimal, NIP, stability, ordered group

Full text: pdf, dvi, ps. (Version of 3 July 2009: pdf, dvi, ps).