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On quasiminimal excellent classes

Published online by Cambridge University Press:  12 March 2014

Jonathan Kirby
Jonathan Kirby*
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, Il 60607., USA
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Abstract

A careful exposition of Zilber's quasiminimal excellent classes and their categoricity is given, leading to two new results: the Lω1ω(Q)-definability assumption may be dropped, and each class is determined by its model of dimension ℵ0.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 2 , June 2010 , pp. 551 - 564
Copyright
Copyright © Association for Symbolic Logic 2010

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References

REFERENCES

[Bal09]Baldwin, John T., Categoricity, University Lecture Series, vol. 50, American Mathematical Society, Providence, RI, 2009.Google Scholar
[Mar02]Marker, David, Model theory: An introduction, Graduate Texts in Mathematics, vol. 217, Springer-Verlag, New York, 2002.Google Scholar
[Zil05]Zilber, Boris, A categoricity theorem for quasi-minimal excellent classes, Logic and its applications (Providence, RI), Contemporary Mathematics, vol. 380, American Mathematical Society, 2005, pp. 297–306.CrossRefGoogle Scholar