On genericity and weight in the free group

Anand Pillay
2009 Proceedings of the American Mathematical Society  
We prove that the generic type of the (theory of the) free group F n on n ≥ 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.
doi:10.1090/s0002-9939-09-09956-0 fatcat:oldui5pklbbrdacokhsmgsvgai