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The Tarski Problems and Their Solutions
2015
Advances in Pure Mathematics
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 has been actually proved. We then discuss the history of the solution
doi:10.4236/apm.2015.54023
fatcat:35xxoyikn5hxhgepie5ptryryi