# 2006 seminar talk: All creatures great and small

Talk held by Martin Goldstern (TU Wien) at the KGRC seminar on 2006-03-30.

### Abstract

For any regular uncountable cardinal lambda I will describe a
"creature-based" lambda^+-complete forcing notion that introduces
a "wild" ultrafilter on lambda.

Assuming 2^lambda=lambda^+, we can find a sufficiently generic
filter on this forcing notion; this allows us to construct a
clone on lambda which is not contained in any coatom of the clone
lattice, solving an old problem in clone theory.
(These notions will be explained in the talk.)

I have sketched a corresponding result for lambda=omega in my talk in November 2002. Both results are a joint work with Saharon Shelah.

I will give a related talk (that concentrates on the algebraic rather than set-theoretic background) in the algebra seminar at TU Wien on April 7, 2006. [1]