Constructive Quantifier Elimination with a Focus on Matrix Rings

Maximilian Illmer; Tim Netzer

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arXiv · 2503.18618

Constructive Quantifier Elimination with a Focus on Matrix Rings

Maximilian Illmer·Tim Netzer

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Abstract

We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for certain matrix rings. The original proof uses model theory, and while it is very elegant and insightful, the proof we propose is much shorter and provides a constructive algorithm.

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Maximilian Illmer, Tim Netzer. 2025-03-24. Constructive Quantifier Elimination with a Focus on Matrix Rings. https://arxiv.org/abs/2503.18618

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