On n-dependent groups and fields III. Multilinear forms and invariant
connected components
On n-dependent groups and fields III. Multilinear forms and invariant
connected components
We develop some model theory of multi-linear forms, generalizing Granger in the bi-linear case. In particular, after proving a quantifier elimination result, we show that for an NIP field K, the theory of infinite dimensional non-degenerate alternating n-linear spaces over K is strictly n-dependent; and it is NSOP1 if K …