Kurt Gödel Research Center

2007 seminar talk: Quagmire forcing

Talk held by Andrew Brooke-Taylor (KGRC) at the KGRC seminar on 2007-01-25.

Abstract

When trying to preserve large cardinals while doing class forcing, a standard trick is to obtain a "mastercondition" - a single condition that the generic must lie below to guarantee that the large cardinal is preserved. If the forcing is homogeneous enough, this choice of an appropriate generic can be performed "after the fact", in the extension V[G] by any generic.

However, the standard forcing to give morasses does not enjoy this sort of homogeneity. We shall show how to modify it so that it does, and in doing so, produce morasses with an extra property.