Every 1-Generic Computes a Properly 1-Generic

by Barbara F. Csima, Rod Downey, Noam Greenberg, Denis R. Hirschfeldt, and Joseph S. Miller

Status: published in the Journal of Symbolic Logic 71 (2006) 1385 - 1393.

Availability: journal version and preprint

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>1 then an m-generic real cannot compute a properly n-generic real.