2025/09/02 by Carl, Merlin
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2509.02766
In arXiv:1811.11630, we introduced a notion of effective reducibility between set-theoretical Π2-statements; in arXiv:2411.19386, this was extended to statements of arbitrary (potentially even infinite) quantifier complexity. We also considered a corresponding notion of Weihrauch reducibility, which allows only one call to the effectivizer of ψ in a reduction of ϕ to ψ. In this paper, we refine this notion considerably by asking how many calls to an effectivizer for ψ are required for effectivizing ϕ. This allows us make formally precise questions such as ``how many ordinals does one need to check for being cardinals in order to compute the cardinality of a given ordinal?'' and (partially) answer many of them. Many of these anwers turn out to be independent of ZFC.