Abstract
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 \(\mathfrak {s}=\mathfrak {b}=\mathfrak {d}<\mathfrak {r}\).KeywordsForcing NotionCohen ForcingSacks ForcingSacks RealsReal SilverThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
