At the end of the paper, a rather unfavourable referee’s report is appended which laments the paucity of the results proved. Indeed, few questions about the model theory of the free group are answered, or even considered. Nevertheless, the author expounds in his usual eloquent French style a very basic theory of generic sets for the free group in countably many generators, which may be helpful in understanding the free group on one hand, and the notion of genericity is a stable group on the other. As knowledge of the definable sets a free group is scarce, he takes recourse to sets invariant under all automorphisms fixing a finite set of group elements; such a set is called generic if it contains infinitely many generators. Generic sets satisfy the usual properties (if \(X\) is not generic, its complement is, and the intersection of two generic sets is again generic); however, the problem of uniformity (for definable sets) and hence preservation of these results under elementary extensions is left open. Finally, another notion of genericity is considered, where a set is generic if finitely many (left, right, or two- sided) translates of it cover the whole group, and the connections with the previous definition are looked at.
For the entire collection see [Zbl 0786.00032].