A Characterization of Strongly Dependent Ordered Abelian Groups

Alfred Dolich; John Goodrick

doi:10.15446/recolma.v52n2.77154

Publicado

2018-07-01

A Characterization of Strongly Dependent Ordered Abelian Groups

Una caracterización de los grupos abelianos fuertemente dependientes

DOI:

https://doi.org/10.15446/recolma.v52n2.77154

Palabras clave:

Strongly dependent theories, NIP, ordered Abelian groups (en)
Teorías dependientes, grupos abelianos ordenados (es)

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Autores/as

Alfred Dolich Kingsborough Community College
John Goodrick Universidad de los Andes

Resumen (en)
Resumen (es)

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].

Damos una caracterización completa de los grupos abelianos ordenados cuyas teorías completas en el lenguaje {+, <, 0} son fuertamente dependientes. El resultado principal de este artículo fue obtenido de manera independiente por Halevi y Hasson [7] y Farré [5].

Referencias

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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.

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

Y. Gurevich and P. H. Schmitt, The theory of ordered abelian groups does not have the independence property, Transactions of the American Mathematical Society 284 (1984), no. 1, 171–182.

Y. Halevi and A. Hasson, Strongly dependent ordered abelian groups and henselian ﬁelds, arXiv: 1706.03376, 2017.

F. Jahnke, P. Simon, and E. Walsberg, Dp-minimal valued ﬁelds, Journal of Symbolic Logic 82 (2015), 151–165.

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S. Shelah, Strongly dependent theories, Israel Journal of Mathematics 204 (2014), 1–83.

Cómo citar

APA

Dolich, A. y Goodrick, J. (2018). A Characterization of Strongly Dependent Ordered Abelian Groups. Revista Colombiana de Matemáticas, 52(2), 139–159. https://doi.org/10.15446/recolma.v52n2.77154

ACM

[1]

Dolich, A. y Goodrick, J. 2018. A Characterization of Strongly Dependent Ordered Abelian Groups. Revista Colombiana de Matemáticas. 52, 2 (jul. 2018), 139–159. DOI:https://doi.org/10.15446/recolma.v52n2.77154.

ACS

(1)

Dolich, A.; Goodrick, J. A Characterization of Strongly Dependent Ordered Abelian Groups. rev.colomb.mat 2018, 52, 139-159.

ABNT

DOLICH, A.; GOODRICK, J. A Characterization of Strongly Dependent Ordered Abelian Groups. Revista Colombiana de Matemáticas, [S. l.], v. 52, n. 2, p. 139–159, 2018. DOI: 10.15446/recolma.v52n2.77154. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/77154. Acesso em: 16 abr. 2025.

Chicago

Dolich, Alfred, y John Goodrick. 2018. «A Characterization of Strongly Dependent Ordered Abelian Groups». Revista Colombiana De Matemáticas 52 (2):139-59. https://doi.org/10.15446/recolma.v52n2.77154.

Harvard

Dolich, A. y Goodrick, J. (2018) «A Characterization of Strongly Dependent Ordered Abelian Groups», Revista Colombiana de Matemáticas, 52(2), pp. 139–159. doi: 10.15446/recolma.v52n2.77154.

IEEE

[1]

A. Dolich y J. Goodrick, «A Characterization of Strongly Dependent Ordered Abelian Groups», rev.colomb.mat, vol. 52, n.º 2, pp. 139–159, jul. 2018.

MLA

Dolich, A., y J. Goodrick. «A Characterization of Strongly Dependent Ordered Abelian Groups». Revista Colombiana de Matemáticas, vol. 52, n.º 2, julio de 2018, pp. 139-5, doi:10.15446/recolma.v52n2.77154.

Turabian

Dolich, Alfred, y John Goodrick. «A Characterization of Strongly Dependent Ordered Abelian Groups». Revista Colombiana de Matemáticas 52, no. 2 (julio 1, 2018): 139–159. Accedido abril 16, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/77154.

Vancouver

1.

Dolich A, Goodrick J. A Characterization of Strongly Dependent Ordered Abelian Groups. rev.colomb.mat [Internet]. 1 de julio de 2018 [citado 16 de abril de 2025];52(2):139-5. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/77154

Descargar cita

CrossRef Cited-by

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1. Will Johnson. (2021). Dp-finite fields I(B): Positive characteristic. Annals of Pure and Applied Logic, 172(6), p.102949. https://doi.org/10.1016/j.apal.2021.102949.

2. ARTEM CHERNIKOV, ALEX MENNEN. (2025). SEMI-EQUATIONAL THEORIES. The Journal of Symbolic Logic, 90(1), p.391. https://doi.org/10.1017/jsl.2023.28.

3. Alfred Dolich, John Goodrick. (2023). Topological properties of definable sets in ordered Abelian groups of burden 2. Mathematical Logic Quarterly, 69(2), p.147. https://doi.org/10.1002/malq.202200052.

4. Yatir Halevi, Assaf Hasson. (2019). Strongly dependent ordered abelian groups and Henselian fields. Israel Journal of Mathematics, 232(2), p.719. https://doi.org/10.1007/s11856-019-1885-3.

5. Matthias Aschenbrenner, Artem Chernikov, Allen Gehret, Martin Ziegler. (2022). Distality in valued fields and related structures. Transactions of the American Mathematical Society, 375(7), p.4641. https://doi.org/10.1090/tran/8661.