A constructive proof of Tarski's theorem on quantifier elimination in the theory of ACF

Grzegorz Pastuszak

A constructive proof of Tarski's theorem on quantifier elimination in the theory of ACF

Logic 2016-07-20 v1 Mathematical Physics math.MP

Authors: Grzegorz Pastuszak

Abstract

Assume that $ACF$ denotes the theory of algebraically closed fields. The renowned theorem of A. Tarski states that $ACF$ admits quantifier elimination. In this paper we give a constructive proof of Tarski's theorem on quantifier elimination in $ACF$ . This means that for a given formula $\varphi$ of the language of fields we construct a quantifier-free formula $\varphi'$ such that $ACF\vdash\varphi\leftrightarrow\varphi'$ . We devote the last section of the paper to show some applications of this constructive version in mathematics and physics.

Keywords

quantifier elimination algebraically closed fields Tarski's theorem constructive proof quantifier-free formula model theory applications

Cite

@article{arxiv.1607.05505,
  title  = {A constructive proof of Tarski's theorem on quantifier elimination in the theory of ACF},
  author = {Grzegorz Pastuszak},
  journal= {arXiv preprint arXiv:1607.05505},
  year   = {2016}
}

A constructive proof of Tarski's theorem on quantifier elimination in the theory of ACF

Abstract

Keywords

Cite

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