On the Generic Type of the Free Group

Details On the Generic Type of the Free Group On the Generic Type of the Free Group

2010-11-14

arxiv.org/abs/1011.3178v1

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

Mathematics

Logic

To appear in J. of Symbolic Logic

Scientific paper

10.2178/jsl/1294170997

We answer a question raised by Pillay, that is whether the infinite weight of the generic type of the free group is witnessed in $F_{\omega}$. 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 $\aleph_1$-homogeneous.

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