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math.LO2025
Failure Modes for Structural Highness Notions
Wesley Calvert, Johanna N. Y. Franklin, Dan Turetsky
In a previous paper, entitled "Structural Highness Notions," we defined several classes of degrees that are high in senses related to computable structure theory. Each class of deg…
math.LO2025
Normality, Relativization, and Randomness
Wesley Calvert, Emma Grunner, Elvira Mayordomo +2
Normal numbers were introduced by Borel and later proven to be a weak notion of algorithmic randomness. We introduce here a natural relativization of normality based on generalized…