Generalized Effective Reducibility

Abstract: We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch reducibility. We give sample applications by showing that certain (algebraic) constructions are not effective in the OTM-sense and considerung the effective equivalence of various versions of the axiom of choice.