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• W2897554237 abstract "In this paper natural necessary and sufficient conditions for quantifier elimination of matrix rings $M_n(K)$ in the language of rings expanded by two unary functions, naming the trace and transposition, are identified. This is used together with invariant theory to prove quantifier elimination when $K$ is an intersection of real closed fields. On the other hand, it is shown that finding a natural textit{definable} expansion with quantifier elimination of the theory of $M_n(C)$ is closely related to the infamous simultaneous conjugacy problem in matrix theory. Finally, for various natural structures describing dimension-free matrices it is shown that no such elimination results can hold by establishing undecidability results." @default.
• W2897554237 created "2018-10-26" @default.
• W2897554237 creator A5039346896 @default.
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• W2897554237 date "2018-10-21" @default.
• W2897554237 modified "2023-09-27" @default.
• W2897554237 title "A Model Theoretic Perspective on Matrix Rings" @default.
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