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3 Quantifier elimination algorithm to boolean combination of ∃∀-formulas in the theory of a free group

Olga Kharlampovich and Alexei Myasnikov

Abstract

It was proved by Sela and by the authors that every formula in the theory of a nonabelian free group F is equivalent to a boolean combination of ∃∀-formulas. We also proved that the elementary theory of a free group is decidable (there is an algorithm given a sentence to decide whether this sentence belongs to Th(F)). Here we describe an algorithm for the reduction of a first-order formula over a free group to the equivalent boolean combination of ∃∀-formulas.

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