Diophantine geometry over groups V1: Quantifier elimination I

Z. Sela*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

19 Scopus citations

Abstract

This paper is the first part (out of two) of the fifth paper in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the two papers on quantifier elimination we use the iterative procedure that validates the correctness of an AE sentence defined over a free group, presented in the fourth paper, to show that the Boolean algebra of AE sets defined over a free group is invariant under projections, and hence show that every elementary set defined over a free group is in the Boolean algebra of AE sets. The procedures we use for quantifier elimination, presented in this paper and its successor, enable us to answer affirmatively some of Tarski's questions on the elementary theory of a free group in the sixth paper of this sequence.

Original languageAmerican English
Pages (from-to)1-197
Number of pages197
JournalIsrael Journal of Mathematics
Volume150
DOIs
StatePublished - 2005

Bibliographical note

Funding Information:
* Partially supported by an Israel Academy of Sciences Fellowship.

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