A Characterization of Strongly Dependent Ordered Abelian Groups-Reference-Cited by-同舟云学术

A Characterization of Strongly Dependent Ordered Abelian Groups

Published:2018-07-01 Issue:2 Volume:52 Page:139-159
ISSN:2357-4100
Container-title:Revista Colombiana de Matemáticas
language:
Short-container-title:rev.colomb.mat

Author:

Dolich Alfred,Goodrick John

Abstract

We characterize all ordered Abelian groups whose ﬁrst-order theory in the language {+, <, 0} is strongly dependent. The main result of this note was obtained independently by Halevi and Hasson [7] and Farré [5].

Publisher

Universidad Nacional de Colombia

Subject

General Mathematics

Reference10 articles.

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2. A. Chernikov, I. Kaplan, and P. Simon, Groups and ﬁelds with NTP2, Proceedings of the American Mathematical Society 143 (2015), no. 1, 395–406.

3. R. Cluckers and I. Halupczok, Quantiﬁer elimination in ordered abelian groups, Conﬂuentes Mathematici 3 (2011), no. 4, 587–615.

4. A. Dolich, J. Goodrick, and D. Lippel, Dp-minimal theories: basic facts and examples, Notre Dame Journal of Formal Logic 52 (2011), no. 3, 267– 288.

5. R. Farré, Strong ordered abelian groups and dp-rank, arXiv: 1706.05471, 2017.

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