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arXiv · 1207.1900

Quantifier elimination algorithm to boolean combination of $\exists\forall$-formulas in the theory of a free group

Olga Kharlampovich·Alexei Myasnikov
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Abstract

It was proved by Sela and by the authors that every formula in the theory of a free group $F$ is equivalent to a boolean combination of $\exists\forall$-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 $Th(F)$). In this paper we give an algorithm for reduction of a first order formula over a free group to an equivalent boolean combination of $\exists\forall$-formulas.

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Olga Kharlampovich, Alexei Myasnikov. 2012-07-08. Quantifier elimination algorithm to boolean combination of $\exists\forall$-formulas in the theory of a free group. https://arxiv.org/abs/1207.1900

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