Silver-Like Forcing Notions

  • Lorenz J. Halbeisen
Part of the Springer Monographs in Mathematics book series (SMM)


On the one hand, we have seen that every forcing notion which adds dominating reals also adds splitting reals (see Fact 20.1). On the other hand, we have seen in the previous chapter that Cohen forcing is a forcing notion which adds splitting reals, but which does not add dominating reals. However, Cohen forcing adds unbounded reals and as an application we constructed a model in which \(\mathfrak {s}=\mathfrak {b}<\mathfrak {d}=\mathfrak {r}\). One might ask whether there exists a forcing notion which is even ω ω-bounding but still adds splitting reals. In this chapter, we shall present such a forcing notion and as an application we shall construct a model in which \(\mathfrak {s}=\mathfrak {b}=\mathfrak {d}<\mathfrak {r}\).


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© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland

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