Ramsey ultrafilters and the reaping number---${\rm Con}({\mathfrak r}<{\mathfrak u})$

by Goldstern and Shelah. [GoSh:388]
Annals Pure and Applied Logic, 1990
We show that the reaping number r is consistenly smaller than the smallest base of an ultrafilter. We use a forcing notion P_U that destroys a selected ultrafilter U and all ultrafilters below it, but preserves all Ramsey ultrafilters that are not below U in the Rudin-Keisler order.

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