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On the generic type of the free group

Published online by Cambridge University Press:  12 March 2014

Rizos Sklinos
Rizos Sklinos*
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail: rsklinos@maths.leeds.ac.uk
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Abstract

We answer a question raised in [9], that is whether the infinite weight of the generic type of the free group is witnessed in Fω. We also prove that the set of primitive elements in finite rank free groups is not uniformly definable. As a corollary, we observe that the generic type over the empty set is not isolated. Finally, we show that uncountable free groups are not ℵ1-homogeneous.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 227 - 234
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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