  We show that results of Akama, Berardi, Hayashi and Kohlenbach, on the
relative independence of certain arithmetical principles over intuitionistic
arithmetic HA, hold also over Kleene and Vesley's system FIM of intuitionistic
analysis, which extends HA and is consistent with classical arithmetic but not
with classical analysis. The double negations of the universal closures of
these principles are also considered, and shown to behave differently with
respect to HA and FIM. Various elementary questions are left open.
