The Elementary Theory of Groups : : A Guide through the Proofs of the Tarski Conjectures / / Benjamin Fine, Anthony Gaglione, Alexei Myasnikov, Gerhard Rosenberger, Dennis Spellman.
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 method...
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Fine, Benjamin, author. aut http://id.loc.gov/vocabulary/relators/aut The Elementary Theory of Groups : A Guide through the Proofs of the Tarski Conjectures / Benjamin Fine, Anthony Gaglione, Alexei Myasnikov, Gerhard Rosenberger, Dennis Spellman. Berlin ; Boston : De Gruyter, [2014] ©2014 1 online resource (307 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Expositions in Mathematics , 0938-6572 ; 60 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Combinatorial analysis. Geometry, Algebraic. Proof theory. Geometrische Gruppentheorie. Gruppentheorie. Kombinatorische Gruppentheorie. Logik. MATHEMATICS / Algebra / Abstract. bisacsh Gaglione, Anthony, author. aut http://id.loc.gov/vocabulary/relators/aut Myasnikov, Alexei, author. aut http://id.loc.gov/vocabulary/relators/aut Rosenberger, Gerhard, author. aut http://id.loc.gov/vocabulary/relators/aut Spellman, Dennis, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package 9783110494969 ZDB-23-EXM Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter EBOOK PACKAGE Complete Package 2014 9783110369526 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics, Physics 2014 9783110370355 ZDB-23-DEM EPUB 9783110382570 print 9783110341997 https://doi.org/10.1515/9783110342031 https://www.degruyter.com/isbn/9783110342031 Cover https://www.degruyter.com/document/cover/isbn/9783110342031/original |
language |
English |
format |
eBook |
author |
Fine, Benjamin, Fine, Benjamin, Gaglione, Anthony, Myasnikov, Alexei, Rosenberger, Gerhard, Spellman, Dennis, |
spellingShingle |
Fine, Benjamin, Fine, Benjamin, Gaglione, Anthony, Myasnikov, Alexei, Rosenberger, Gerhard, Spellman, Dennis, The Elementary Theory of Groups : A Guide through the Proofs of the Tarski Conjectures / De Gruyter Expositions in Mathematics , 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 |
author_facet |
Fine, Benjamin, Fine, Benjamin, Gaglione, Anthony, Myasnikov, Alexei, Rosenberger, Gerhard, Spellman, Dennis, Gaglione, Anthony, Gaglione, Anthony, Myasnikov, Alexei, Myasnikov, Alexei, Rosenberger, Gerhard, Rosenberger, Gerhard, Spellman, Dennis, Spellman, Dennis, |
author_variant |
b f bf b f bf a g ag a m am g r gr d s ds |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Gaglione, Anthony, Gaglione, Anthony, Myasnikov, Alexei, Myasnikov, Alexei, Rosenberger, Gerhard, Rosenberger, Gerhard, Spellman, Dennis, Spellman, Dennis, |
author2_variant |
a g ag a m am g r gr d s ds |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Fine, Benjamin, |
title |
The Elementary Theory of Groups : A Guide through the Proofs of the Tarski Conjectures / |
title_sub |
A Guide through the Proofs of the Tarski Conjectures / |
title_full |
The Elementary Theory of Groups : A Guide through the Proofs of the Tarski Conjectures / Benjamin Fine, Anthony Gaglione, Alexei Myasnikov, Gerhard Rosenberger, Dennis Spellman. |
title_fullStr |
The Elementary Theory of Groups : A Guide through the Proofs of the Tarski Conjectures / Benjamin Fine, Anthony Gaglione, Alexei Myasnikov, Gerhard Rosenberger, Dennis Spellman. |
title_full_unstemmed |
The Elementary Theory of Groups : A Guide through the Proofs of the Tarski Conjectures / Benjamin Fine, Anthony Gaglione, Alexei Myasnikov, Gerhard Rosenberger, Dennis Spellman. |
title_auth |
The Elementary Theory of Groups : A Guide through the Proofs of the Tarski Conjectures / |
title_alt |
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 |
title_new |
The Elementary Theory of Groups : |
title_sort |
the elementary theory of groups : a guide through the proofs of the tarski conjectures / |
series |
De Gruyter Expositions in Mathematics , |
series2 |
De Gruyter Expositions in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2014 |
physical |
1 online resource (307 p.) Issued also in print. |
contents |
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 |
isbn |
9783110342031 9783110494969 9783110238570 9783110238471 9783110637205 9783110369526 9783110370355 9783110382570 9783110341997 |
issn |
0938-6572 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA565 |
callnumber-sort |
QA 3565 E44 42014EB |
url |
https://doi.org/10.1515/9783110342031 https://www.degruyter.com/isbn/9783110342031 https://www.degruyter.com/document/cover/isbn/9783110342031/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512.2 |
dewey-sort |
3512.2 |
dewey-raw |
512.2 |
dewey-search |
512.2 |
doi_str_mv |
10.1515/9783110342031 |
oclc_num |
894739867 |
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Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter EBOOK PACKAGE Complete Package 2014 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics, Physics 2014 |
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The Elementary Theory of Groups : A Guide through the Proofs of the Tarski Conjectures / |
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