Norms on Possibilities I: Forcing with Trees and Creatures, Issue 671

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American Mathematical Society, Sep 1, 1999 - Mathematics - 167 pages
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Abstract. In this Memoir we present a systematic study of the method of norms on possibilities of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the solutions we develop various ideas interesting per se. These include a new iterable condition for ``not adding Cohen reals'' (which has a flavour of preserving special properties of $p$-points), new intriguing properties of ultrafilters (weaker than being Ramsey but stronger than $p$-point) and some new applications of variants of the PP-property.

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