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We show that results of Akama, Berardi, Hayashi and Kohlenbach, on therelative independence of certain arithmetical principles over intuitionisticarithmetic HA, hold also over Kleene and Vesley's system FIM of intuitionisticanalysis, which extends HA and is consistent with classical arithmetic but notwith classical analysis. The double negations of the universal closures ofthese principles are also considered, and shown to behave differently withrespect to HA and FIM. Various elementary questions are left open.

Note on $\Pi^0_{n+1}$-LEM, $\Sigma^0_{n+1}$-LEM and $\Sigma^0_{n+1}$-DNE