Journal of Symbolic Logic

On the generic type of the free group

Rizos Sklinos

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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.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 1 (2011), 227-234.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1294170997

Digital Object Identifier
doi:10.2178/jsl/1294170997

Mathematical Reviews number (MathSciNet)
MR2791345

Zentralblatt MATH identifier
1213.03047

Citation

Sklinos, Rizos. On the generic type of the free group. J. Symbolic Logic 76 (2011), no. 1, 227--234. doi:10.2178/jsl/1294170997. https://projecteuclid.org/euclid.jsl/1294170997


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