Publicado

2018-07-01

A Characterization of Strongly Dependent Ordered Abelian Groups

Una caracterización de los grupos abelianos fuertemente dependientes

Palabras clave:

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

Autores/as

  • Alfred Dolich Kingsborough Community College
  • John Goodrick Universidad de los Andes
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].

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Citas

H. Adler, Strong theories, burden, and weight, available on author’s website, 2007.

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

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

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.

S. Shelah, Classification theory, second ed., North-Holland, 1990.

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