03498nam 2200685 450 991046479070332120210422203031.03-11-038257-13-11-034203-010.1515/9783110342031(CKB)3520000000004117(EBL)1663235(SSID)ssj0001432759(PQKBManifestationID)11886066(PQKBTitleCode)TC0001432759(PQKBWorkID)11405805(PQKB)10610467(MiAaPQ)EBC1663235(DE-B1597)245801(OCoLC)894739867(OCoLC)979955115(DE-B1597)9783110342031(Au-PeEL)EBL1663235(CaPaEBR)ebr11010164(CaONFJC)MIL806993(EXLCZ)99352000000000411720150211h20142014 uy 0engur|nu---|u||utxtccrThe elementary theory of groups a guide through the proofs of the Tarski conjectures /Benjamin Fine [and five others]Berlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2014.©20141 online resource (322 p.)De Gruyter Expositions in Mathematics,0938-6572 ;Volume 60Description based upon print version of record.3-11-034199-9 Includes bibliographical references and index.Front matter --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 square like groups --References --IndexAfter 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. Both proofs involve long and complicated applications of algebraic geometry over free groups as well as an extension of methods to solve equations in free groups originally developed by Razborov. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. This material includes a complete exposition of the theory of fully residually free groups or limit groups as well a complete description of the algebraic geometry of free groups. Also included are introductory material on combinatorial and geometric group theory and first-order logic. There is then a short outline of the proof of the Tarski conjectures in the manner of Kharlampovich and Myasnikov.De Gruyter expositions in mathematics ;Volume 60.Geometry, AlgebraicCombinatorial analysisProof theoryElectronic books.Geometry, Algebraic.Combinatorial analysis.Proof theory.512/.2Fine Benjamin, 56763Fine Benjamin1948-MiAaPQMiAaPQMiAaPQBOOK9910464790703321The elementary theory of groups2461128UNINA