The elementary theory of groups : a guide through the proofs of the Tarski conjectures

After Being An Open Question For Sixty Years The Tarski Conjecture Was Answered In The Affirmative By Olga Kharlampovich And Alexei Myasnikov And Independently By Zlil Sela. This Book Is An Examination Of The Material On The General Elementary Theory Of Groups That Is Necessary To Begin To Understand The Proofs. Frontmatter -- Preface -- Contents -- 1 Group Theory And Logic: Introduction -- 2 Combinatorial Group Theory -- 3 Geometric Group Theory -- 4 First Order Languages And Model Theory -- 5 The Tarski Problems -- 6 Fully Residually Free Groups I -- 7 Fully Residually Free Groups Ii -- 8 Algebraic Geometry Over Groups -- 9 The Solution Of The Tarski Problems -- 10 On Elementary Free Groups And Extensions -- 11 Discriminating And Squarelike Groups -- References -- Index. Benjamin Fine [and Four Others]. Includes Bibliographical References And Index. After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. B. Fine, Fairfield U.; A. Gaglione, US Naval Academy; A. Myasnikov, McGill U.; G. Rosenberger, U. of Passau;D. Spellman, Temple U