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AISC
2010
Springer

A Formal Quantifier Elimination for Algebraically Closed Fields

8 years 11 months ago
A Formal Quantifier Elimination for Algebraically Closed Fields
We prove formally that the first order theory of algebraically closed fields enjoy quantifier elimination, and hence is decidable. This proof is organized in two modular parts. We first reify the first order theory of rings and prove that quantifier elimination leads to decidability. Then we implement an algorithm which constructs a quantifier free formula from any first order formula in the theory of ring. If the underlying ring is in fact an algebraically closed field, we prove that the two formulas have the same semantic. The algorithm producing the quantifier free formula is programmed in continuation passing style, which leads to both a concise program and an elegant proof of semantic correctness.
Cyril Cohen, Assia Mahboubi
Added 02 Sep 2010
Updated 02 Sep 2010
Type Conference
Year 2010
Where AISC
Authors Cyril Cohen, Assia Mahboubi
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