English

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

Group Theory 2019-09-13 v4

Abstract

It was proved by Sela and by the authors that every formula in the theory of a free group FF 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)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.

Keywords

Cite

@article{arxiv.1207.1900,
  title  = {Quantifier elimination algorithm to boolean combination of $\exists\forall$-formulas in the theory of a free group},
  author = {Olga Kharlampovich and Alexei Myasnikov},
  journal= {arXiv preprint arXiv:1207.1900},
  year   = {2019}
}

Comments

In this version we describe in more details the algorithm from our paper "Elementary theory of free non-abelian groups" (J. Algebra, 302, 2006). We also corrected some misprints and non-essential errors in "Elementary theory of free non-abelian groups" noticed by different people