Abstract
We introduce two notions of effective reducibility for settheoretical 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 considering the effective equivalence of various versions of the axiom of choice.
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CITATION STYLE
Carl, M. (2016). Generalized effective reducibility. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9709, pp. 225–233). Springer Verlag. https://doi.org/10.1007/978-3-319-40189-8_23
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