Every 1-Generic Computes a Properly 1-Generic
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.