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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: zou@math.univ-lyon1.fr
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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

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