Mathias forcing which does not add dominating reals. (English) Zbl 0691.03030
Summary: Assume that there is no dominating family of reals of cardinality \(<{\mathfrak c}\). We show that there then exists an ultrafilter on the set of natural numbers such that its associated Mathias forcing does not adjoin any real which dominates all ground model reals. Such ultrafilters are necessarily P-points with no Q-points below them in the Rudin-Keisler order.
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