Every 1-generic computes a properly 1-generic
Barbara F. Csima, Rodney G. Downey, Noam Greenberg, Denis R. Hirschfeldt, Joseph S. Miller · Journal of Symbolic Logic · 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.