Elementary theory of free non-abelian groups

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 2006 English Publisher:Elsevier BVJournal:Journal of Algebra, volume 302, pages 451-552 (issn: 0021-8693,

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Authors: Kharlampovich, Olga; Myasnikov, Alexei;

doi: 10.1016/j.jalgebra.2006.03.033

Elementary theory of free non-abelian groups

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Abstract

For a group \(G,\) the elementary theory \(\text{Th}(G)\) of \(G\) is the set of all first-order sentences in the language of group theory which are true in \(G.\) Around 1945 Tarski formulated two conjectures about the elementary theory of a free group. The first of them states that the elementary theory of non-abelian free groups of different ranks coincide; the second one states that the elementary theory of free groups is decidable. The scope of this paper is to prove these two conjectures.

Related Organizations

McGill University
Canada

Keywords

decidable theory, Decidability of theories and sets of sentences, Algebra and Number Theory, elementary theory, free group, Free group, Free nonabelian groups, Elementary theory, Applications of logic to group theory, Models of other mathematical theories

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