Every 1-Generic Computes a Properly 1-Generic

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Journal of Symbolic Logic 71 (4):1385 - 1393 (2006)
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Abstract

A real is called properly n-generic if it is n-generic but not n+1-generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n ≥ 2 then an m-generic real cannot compute a properly n-generic real

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10.2178/jsl/1164060461

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Calibrating randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
Lowness for genericity.Liang Yu - 2006 - Archive for Mathematical Logic 45 (2):233-238.
Embedding and Coding below a 1-Generic Degree.Noam Greenberg & Antonio Montalbán - 2003 - Notre Dame Journal of Formal Logic 44 (4):200-216.

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