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PSEUDOFINITE H-STRUCTURES AND GROUPS DEFINABLE IN SUPERSIMPLE H-STRUCTURES

Published online by Cambridge University Press:  02 April 2019

TINGXIANG ZOU
TINGXIANG ZOU*
Affiliation:
INSTITUT CAMILLE JORDAN UNIVERSITÉ CLAUDE BERNARD LYON 1 69622 VILLEURBANNE CEDEX, FRANCEE-mail: [email protected]
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Abstract

In this article we explore some properties of H-structures which are introduced in [2]. We describe a construction of H-structures based on one-dimensional asymptotic classes which preserves pseudofiniteness. That is, the H-structures we construct are ultraproducts of finite structures. We also prove that under the assumption that the base theory is supersimple of SU-rank one, there are no new definable groups in H-structures. This improves the corresponding result in [2].

Keywords

03C20H-structuresone-dimensional asymptotic classsupsersimple theorydefinable group
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 3 , September 2019 , pp. 937 - 956
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

REFERENCES

Berenstein, A. and Vassiliev, E., On lovely pairs of geometric structures. Annals of Pure and Applied Logic, vol. 161 (2010), no. 7, pp. 866–878.Google Scholar
Berenstein, A. and Vassiliev, E., Geometric structures with a dense independent subset. Selecta Mathematica, vol. 22 (2016), no. 1, pp. 191–225.Google Scholar
Duret, J.-L., Les corps faiblement algébriquement clos non séparablement clos ont la propriété d’indépendance, Model Theory of Algebra and Arithmetic (Pacholski, L., Wierzejewski, J., and Wilkie, A. J., editors), Springer, Berlin, 1980, pp. 136–162.Google Scholar
Eleftheriou, P., Characterizing o-minimal groups in tame expansions of o-minimal structures, preprint, 2018, arXiv:1805.11500.Google Scholar
Hrushovski, E. and Pillay, A., Groups definable in local fields and pseudofinite fields. Israel Journal of Mathematics, vol. 85 (1994), no. 1, pp. 203–262.Google Scholar
Macpherson, D. and Steinhorn, C., One-dimensional asymptotic classes of finite structures. Transactions of the American Mathematical Society, vol. 360 (2008), no. 1, pp. 411–448.Google Scholar
Wagner, F. O., Simple Theories, Kluwer Academic Publishers, 2000.Google Scholar