Every 1-generic computes a properly 1-generic

Barbara F. Csima, Rod Downey, Noam Greenberg, Denis R. Hirschfeldt, Joseph S. Miller
2006 Journal of Symbolic Logic (JSL)  
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.
doi:10.2178/jsl/1164060461 fatcat:v5wuewhr4zfgxivpklcxf3l7ci