  We give four different independence relations on any exponential field. Each
is a canonical independence relation on a suitable Abstract Elementary Class of
exponential fields, showing that two of these are NSOP$_1$-like and non-simple,
a third is stable, and the fourth is the quasiminimal pregeometry of Zilber's
exponential fields, previously known to be stable (and uncountably
categorical). We also characterise the fourth independence relation in terms of
the third, strong independence.
