Chernikov's field conjecture on n-dependence and dependence

A field is viewed as a structure in the pure ring language, and $n$-dependence is understood in the model-theoretic sense. Chernikov's field conjecture. If a field is $n$-dependent for some $n \in \omega$, then it is already dependent. This conjecture asks whether fields can exhibit genuinely higher-order dependence; it is attributed to Chernikov and is also posed as a problem in the cited work.