Searching problems above arithmetical transfinite recursion

We investigate some Weihrauch problems between ATR2 and Cωω. We show that the fixed point theorem for monotone operators on the Cantor space (a weaker version of the Knaster-Tarski theorem) is not Weihrauch reducible to ATR2. Furthermore, we introduce the ω-model reflection ATR2rfn of ATR2 and show that it is an upper bound for problems provable from the axiomatic system ATR0 which are of the form ∀X(θ(X)→∃Yη(X,Y)) with arithmetical formulas θ,η. We also show that Weihrauch degrees of relativized least fixed point theorems for monotone operators on the Cantor space form a linear hierarchy between ATR2rfn and Cωω.