Abstract: 

I will present ongoing work joint with Müller, Ramsey and Siniora. A classical result of Macintyre and Saracino states that the theory of Lie algebras over a fixed field and of bounded nilpotency class does not admit a model-companion. We prove that by letting the field grow (i.e. with a separated sort for the field) the theory of Lie algebras of bounded nilpotency class admits a model-companion and that this theory relates asymptotically to the omega-categorical existentially closed c-nilpotent Lie algebra over a finite field F_p for c<p. We also prove that if the theory of the  field is NSOP1 then the theory of the corresponding Lie algebra is NSOP4. We will explain how to get this result via a criterion for NSOP4 which does not use stationary independence relations.

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