Every 1-Generic Computes a Properly 1-Generic

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