Over NIP fields, infinite dimensional alternating n-linear spaces are strictly n-dependent and NSOP1, proved via a new composition lemma for NIP relations and connected-component analysis.
Mekler’s construction preserves CM-triviality.Annals of Pure and Applied Logic, 115(1-3):115–173, 2002
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On n-dependent groups and fields III. Multilinear forms and invariant connected components
Over NIP fields, infinite dimensional alternating n-linear spaces are strictly n-dependent and NSOP1, proved via a new composition lemma for NIP relations and connected-component analysis.