Norms on possibilities I: forcing with trees and creatures

Details Norms on possibilities I: forcing with trees and creatures Norms on possibilities I: forcing with trees and creatures

1998-07-30

arxiv.org/abs/math/9807172v1

Mathematics

Logic

accepted for Memoirs of the Amer. Math. Soc

Scientific paper

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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