Elementary theory of free non-abelian groups.
For a group \(G,\) the elementary theory \(\text{Th}(G)\) of \(G\) is the set of all first-order sentences in the language of group theory which are true in \(G.\) Around 1945 Tarski formulated two conjectures about the elementary theory of a free group. The first of them states that the elementary theory of non-abelian free groups of different ranks coincide; the second one states that the elementary theory of free groups is decidable. The scope of this paper is to prove these two conjectures.
scientific article; zbMATH DE number 5078136
scientific article