Around 1945, Alfred Tarski proposed several questions concerning the elementary theory of nonabelian free groups. These remained open for 60 years until they were proved by O. Kharlampovich and A. Myasnikov and independently by Z. Sela. The proofs, by both sets of authors, were monumental and involved the development of several new areas of infinite group theory. In this paper we explain precisely the Tarski problems and what was actually proved. We then discuss the
history of the solution as well the components of the proof. We then provide the basic startegy for
the proof. We finish with a brief discussion of elementary free groups.

Author (s) Details

Benjamin Fine Department of Mathematics, Faireld University, Faireld, Connecticut 06430, USA.

Anthony Gaglione Department of Mathematics, United States Naval Academy, Annapolis, Maryland 21402, USA.

Gerhard Rosenberger Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany.