Author:
GREENBERG NOAM,MONIN BENOIT
Abstract
We use concepts of continuous higher randomness, developed in Bienvenuet al.[‘Continuous higher randomness’, J. Math. Log. 17(1) (2017).], to investigate$\unicode[STIX]{x1D6F1}_{1}^{1}$-randomness. We discuss lowness for$\unicode[STIX]{x1D6F1}_{1}^{1}$-randomness, cupping with$\unicode[STIX]{x1D6F1}_{1}^{1}$-random sequences, and an analogue of the Hirschfeldt–Miller characterization of weak 2-randomness. We also consider analogous questions for Cohen forcing, concentrating on the class of$\unicode[STIX]{x1D6F4}_{1}^{1}$-generic reals.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
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