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The Elementary Theory of Groups : A Guide Through the Proofs of the Tarski Conjectures

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Title: The Elementary Theory of Groups : A Guide Through the Proofs of the Tarski Conjectures
Description: 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. 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.
Authors: Benjamin Fine, Anthony Gaglione, Alexei Myasnikov, Gerhard Rosenberger, Dennis Spellman
Resource Type: eBook.
Subjects: Geometry, Algebraic, Combinatorial analysis, Proof theory
Categories: MATHEMATICS / Algebra / Abstract, MATHEMATICS / Research
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-epub
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 887060
RelevancyScore: 1057
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1057.36352539063
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  Data: The Elementary Theory of Groups : A Guide Through the Proofs of the Tarski Conjectures
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  Group: Ab
  Data: 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. 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.
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  Data: <searchLink fieldCode="AR" term="%22Benjamin+Fine%22">Benjamin Fine</searchLink><br /><searchLink fieldCode="AR" term="%22Anthony+Gaglione%22">Anthony Gaglione</searchLink><br /><searchLink fieldCode="AR" term="%22Alexei+Myasnikov%22">Alexei Myasnikov</searchLink><br /><searchLink fieldCode="AR" term="%22Gerhard+Rosenberger%22">Gerhard Rosenberger</searchLink><br /><searchLink fieldCode="AR" term="%22Dennis+Spellman%22">Dennis Spellman</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Geometry%2C+Algebraic%22">Geometry, Algebraic</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+analysis%22">Combinatorial analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Proof+theory%22">Proof theory</searchLink>
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      – Code: 512.2
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Geometry, Algebraic
        Type: general
      – SubjectFull: Combinatorial analysis
        Type: general
      – SubjectFull: Proof theory
        Type: general
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      – TitleFull: The Elementary Theory of Groups : A Guide Through the Proofs of the Tarski Conjectures
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            – D: 01
              M: 01
              Type: published
              Y: 2014
            – D: 08
              M: 02
              Type: profile
              Y: 2018
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              Value: 9783110341997
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            – TitleFull: The Elementary Theory of Groups : A Guide Through the Proofs of the Tarski Conjectures
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