On genericity and weight in the free group

Pillay, Anand

doi:10.1090/S0002-9939-09-09956-0

On genericity and weight in the free group
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Proc. Amer. Math. Soc. 137 (2009), 3911-3917 Request permission

Abstract:

We prove that the generic type of the (theory of the) free group $F_{n}$ on $n\geq 2$ generators has infinite weight, strengthening the well-known result that these free groups are not superstable. A preliminary result, possibly of independent interest, is that the realizations in $F_{n}$ of the generic type are precisely the primitives.

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