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A TWO-SORTED THEORY OF NILPOTENT LIE ALGEBRAS
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- Journal:
- The Journal of Symbolic Logic , First View
- Published online by Cambridge University Press:
- 22 July 2025, pp. 1-24
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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 NSOP
$_1$, then the model companion is NSOP
$_4$. We also prove that if the field is algebraically closed, then the model companion is c-NIP.
