Diophantine geometry over groups V_{1}: Quantifier elimination I
 Z. Zela
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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 anAE sentence defined over a free group, presented in the fourth paper, to show that the Boolean algebra ofAE 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 ofAE 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.
 Guba, V. (1986) Equivalence of infinite systems of equations in free groups and semigroups to finite subsystems. Matematicheskie Zametki 40: pp. 321324
 Merzlyakov, Yu. I. (1966) Positive formulae on free groups. Algebra i Logika 5: pp. 257266
 Scott, P. (1978) Subgroups of surface groups are almost geometric. Journal of the London Mathematical Society 17: pp. 555565 CrossRef
 Sela, Z. (2001) Diophantine geometry over groups I: MakaninRazborov diagrams. Publication MathÃ©matiques de l'IHES 93: pp. 31105 CrossRef
 Sela, Z. (2003) Diophantine geometry over groups II: Completions, closures and formal solutions. Israel Journal of Mathematics 134: pp. 173254
 Sela, Z. (2005) Diophantine geometry over groups III: Rigid and solid solutions. Israel Journal of Mathematics 147: pp. 173
 Sela, Z. (2004) Diophantine geometry over groups IV: An interative procedure for validation of a sentence. Israel Journal of Mathematics 143: pp. 1130
 Title
 Diophantine geometry over groups V_{1}: Quantifier elimination I
 Journal

Israel Journal of Mathematics
Volume 150, Issue 1 , pp 1197
 Cover Date
 20051201
 DOI
 10.1007/BF02762378
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
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 Authors

 Z. Zela ^{(1)}
 Author Affiliations

 1. Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, 91904, Jerusalem, Israel