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ISSN 1079-6762

 

Tarski's problem about the elementary theory of free groups has a positive solution


Authors: Olga Kharlampovich and Alexei Myasnikov
Journal: Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 101-108
MSC (1991): Primary 20E05, 20F10; Secondary 03B25, 03C68
Published electronically: December 14, 1998
MathSciNet review: 1662319
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Abstract: We prove that the elementary theories of all nonabelian free groups coincide and that the elementary theory of a free group is decidable. These results answer two old questions that were raised by A. Tarski around 1945.


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Additional Information

Olga Kharlampovich
Affiliation: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montreal, QC, Canada H3A 2K6
Email: olga@Math.McGill.CA

Alexei Myasnikov
Affiliation: Department of Mathematics, City College, Convent Ave. & 138th St., New York, NY 10031
Email: Alexei@rio.sci.ccny.cuny.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-98-00047-X
PII: S 1079-6762(98)00047-X
Keywords: Free group, elementary theory, Tarski
Received by editor(s): May 25, 1998
Published electronically: December 14, 1998
Communicated by: Efim Zelmanov
Article copyright: © Copyright 1998 American Mathematical Society