A Two-Sorted Theory of Nilpotent Lie Algebras

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Mathematics & Actuarial Science Department

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Mathematics & Actuarial Science Department

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Mathematics & Actuarial Science Department

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https://doi.org/10.1017/jsl.2025.10107

All Authors

Christian D'elbée Isabel Müller Nicholas Ramsey Daoud Siniora

Document Type

Research Article

Publication Title

Journal of Symbolic Logic

Publication Date

1-1-2025

doi

10.1017/jsl.2025.10107

Abstract

We prove the existence of a model companion of the two-sorted theory of c-nilpotent Lie algebras over a field satisfying a given theory of fields. We describe a language in which it admits relative quantifier elimination up to the field sort. Using a new criterion which does not rely on a stationary independence relation, we prove that if the field is NSOP1, then the model companion is NSOP4. We also prove that if the field is algebraically closed, then the model companion is c-NIP.

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