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Some remarks on generic structures

Published online by Cambridge University Press:  12 March 2014

David M. Evans  and
Mark Wing Ho Wong
David M. Evans
Affiliation:
University of East Anglia, School of Mathematics, Norwich, Nr4 7Tj, UK, E-mail: d.evans@uea.ac.uk
Mark Wing Ho Wong
Affiliation:
University of East Anglia, School of Mathematics, Norwich, Nr4 7Tj, UK, E-mail: markwwong@yahoo.com
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Abstract

We show that the ℵ0-categorical structures produced by Hrushovski's predimension construction with a control function fit neatly into Shelah's SOPn hierarchy: if they are not simple, then they have SOP3 and NSOP4. We also show that structures produced without using a control function can be undecidable and have SOP.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 4 , December 2009 , pp. 1143 - 1154
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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