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ONE DIMENSIONAL GROUPS DEFINABLE IN THE p-ADIC NUMBERS

Part of: Model theory

Published online by Cambridge University Press:  15 February 2021

JUAN PABLO ACOSTA LÓPEZ
JUAN PABLO ACOSTA LÓPEZ*
Affiliation:
DEPARTMENT OF MATHEMATICS OF THE UNIVERSITY OF MÜNSTER SCHOSSPLATZ 2, 48149MÜNSTER, GERMANYE-mail: [email protected]
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Abstract

A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subgroup and a quotient by a finite subgroup.

Keywords

groupsp-adic numbersmodel theory

MSC classification

Primary: 03C07: Basic properties of first-order languages and structures
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 2 , June 2021 , pp. 801 - 816
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Copyright
© The Association for Symbolic Logic 2021

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References

Acosta, J. P., One dimensional groups definable in the p-adic numbers , Ph.D. thesis, Universidad de los Andes, Bogotá, Colombia, 2019.Google Scholar
Cluckers, R., Pressburger sets and p-minimal fields, this Journal, vol. 68 (2003), pp. 153–162.Google Scholar
Cluckers, R., Analytic p-adic cell decomposition and integrals . Transactions of the American Mathematical Society , vol. 356 (2004), pp. 1489–1499.10.1090/S0002-9947-03-03458-5CrossRefGoogle Scholar
Denef, J., p-adic semi-algebraic sets and cell decomposition . Journal für die Reine und Angewandte Mathematik , vol. 369 (1986), pp. 154–166.Google Scholar
Fremlin, D. H., Measure Theory , vol. 4, Torres Framlin, Colchester, UK, 2013.Google Scholar
Madden, J. J. and Stanton, C. M., One-dimensional nash groups . Pacific Journal of Mathematics , vol. 154 (1992), pp. 331–344.10.2140/pjm.1992.154.331CrossRefGoogle Scholar
Montenegro, S., Onshuus, A., and Simon, P., Stabilizers, groups with f-generics in ${{{NTP}}}_2$ and PRC fields. Journal of the Institute of Mathematics of Jussieu , vol. 19 (2020), no. 3, pp. 821–852.CrossRefGoogle Scholar
Pillay, A., Type-definability, compact Lie groups and o-minimality . Journal of Mathematical Logic , vol. 4 (2004), pp. 147–162.10.1142/S0219061304000346CrossRefGoogle Scholar
Pillay, A. and Onshuus, A., Definable groups and compact p-adic Lie groups . Journal of the London Mathemaical Society , vol. 78 (2008), no. 1, pp. 233–247.Google Scholar
Pillay, A. and Yao, N., A note on groups definable in the p-adic field. Archive for Mathematical Logic , vol. 58 (2019), no. 4, pp. 1029–1034.10.1007/s00153-019-00673-yCrossRefGoogle Scholar
Schneider, P., p-Adic Lie Groups , Springer Science & Business Media, Berlin, Germany, 2011.10.1007/978-3-642-21147-8CrossRefGoogle Scholar
Silverman, J. H., The Arithmetic of Elliptic Curves , Springer, New York, 1986.10.1007/978-1-4757-1920-8CrossRefGoogle Scholar
Silverman, J. H., Advanced Topics in the Arithmetic of Elliptic Curves , Springer, New York, 1994.10.1007/978-1-4612-0851-8CrossRefGoogle Scholar
van den Dries, L., Dimension of definable sets, algebraic boundedness and henselian fields . Annals of Pure and Applied Logic , vol. 45 (1989), pp. 189–209.10.1016/0168-0072(89)90061-4CrossRefGoogle Scholar