Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T02:25:08.713Z Has data issue: false hasContentIssue false
  • English
  • Français

UNIMODULARITY UNIFIED

Published online by Cambridge University Press:  08 May 2017

DARÍO GARCÍA  and
FRANK O. WAGNER
DARÍO GARCÍA
Affiliation:
UNIV LYON, UNIVERSITÉ CLAUDE BERNARD LYON 1 CNRS UMR 5208, INSTITUT CAMILLE JORDAN 43 BLVD. DU 11 NOVEMBRE 1918 F-69622 VILLEURBANNE CEDEX, FRANCE E-mail:d.garcia@leeds.ac.uk
FRANK O. WAGNER
Affiliation:
UNIV LYON, UNIVERSITÉ CLAUDE BERNARD LYON 1 CNRS UMR 5208, INSTITUT CAMILLE JORDAN 43 BLVD. DU 11 NOVEMBRE 1918 F-69622 VILLEURBANNE CEDEX, FRANCE E-mail:wagner@math.univ-lyon1.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied. In particular, it is shown that all notions coincide for non-multidimensional theories where the dimensions are associated to strongly minimal types.

Keywords

03C45unimodularityfunctional unimodularitycorrespondence unimodularitymeasurable typestable theorynon-multidimensional theorystrongly minimal set
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 3 , September 2017 , pp. 1051 - 1065
Copyright
Copyright © The Association for Symbolic Logic 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Elwes, R., Asymptotic classes of finite structures , this Journal, vol. 72 (2007), no. 2, pp. 418–438.Google Scholar
Elwes, R. and Macpherson, D., A survey of asymptotic classes and measurable structures , Model Theory with Applications to Algebra and Analysis, vol. 2 (Chatzidakis, Z., Macpherson, D., Pillay, A., and Wilkie, A., editors), LMS Lecture Notes Series 350, Cambridge University Press, Cambridge, 2008, pp.125–159.CrossRefGoogle Scholar
Ewes, R., Jaligot, E., Macpherson, D., and Ryten, M., Groups in simple and pseudofinite theories . Proceedings of the London Mathematical Society (3), vol. 103 (2011), no. 6, pp. 1049–1082.Google Scholar
Hrushovski, E., Unimodular minimal structures . Journal of the London Mathematical Society, vol. 46 (1992), no. 3, pp. 385–396.Google Scholar
Kestner, C., and Pillay, A., Remarks on unimodularity , this Journal, vol. 76 (2011), no. 4, pp. 1453–1458.Google Scholar
Macpherson, D., and Steinhorn, C., One-dimensional asymptotic classes of finite structures . Transactions of the American Mathematical Society. vol. 360 (2007), pp. 411–448.Google Scholar
Macpherson, D., Definability in classes of finite structures , Finite and Algorithmic Model Theory (Esparza, J., Michaux, C., and Steinhorn, C., editors), London Mathematical Society, No. 379, Cambridge University Press, Cambridge, 2011, pp. 140–176.CrossRefGoogle Scholar
Palacín, D., and Wagner, F. O., Ample thoughts , this Journal, vol. 78 (2013), no. 2, pp. 489–510.Google Scholar
Pillay, A., Geometric Stability Theory, Oxford Logic Guides 32, Clarendon Press, Oxford, 1996.CrossRefGoogle Scholar
Poizat, B., Groupes Stables , Nur al-Mantiq wal-Ma’rifah n. 2, 1987. English translation: Stable Groups , AMS, 2001.Google Scholar
Wagner, F. O., Simple Theories, Mathematics and its Applications 503, Kluwer Academic Publishers, Dordrecht, 2000.Google Scholar