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

Olga Kharlampovich; Alexei Myasnikov

doi:10.1090/S1079-6762-98-00047-X

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

Olga Kharlampovich, Alexei Myasnikov

Department of Mathematical Sciences

McGill University

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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.

Original language	English
Pages (from-to)	101-108
Number of pages	8
Journal	Electronic Research Announcements of the American Mathematical Society
Volume	4
Issue number	14
DOIs	https://doi.org/10.1090/S1079-6762-98-00047-X
State	Published - 14 Dec 1998

Keywords

Elementary theory
Free group
Tarski

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10.1090/S1079-6762-98-00047-X

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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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author = "Olga Kharlampovich and Alexei Myasnikov",

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AU - Myasnikov, Alexei

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N2 - 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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KW - Free group

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JO - Electronic Research Announcements of the American Mathematical Society

JF - Electronic Research Announcements of the American Mathematical Society

IS - 14

ER -

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

Abstract

Keywords

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