HIGHER RANDOMNESS AND GENERICITY
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.
2000 ◽
Vol 90
(3)
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pp. 253-259
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2003 ◽
Vol 88
(5)
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pp. 245-250
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1974 ◽
Vol 32
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pp. 254-255
1983 ◽
Vol 41
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pp. 270-271
1973 ◽
Vol 31
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pp. 144-145
1973 ◽
Vol 31
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pp. 132-133
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1983 ◽
Vol 41
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pp. 194-195
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