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.
Stability theory, permutations of indiscernibles, and embedded finite models.Transactions of the American Mathematical Society, 352(11):4937–4969, 2000
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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.