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On Silver's and Related Principles

DOI: 10.1016/s0049-237x(09)70509-9
  • Logic
  • Mathematics


Publisher Summary This chapter discusses the Silver's Principle (Wk). This principle fits well into the remarkable program initiated by Jensen of formulating useful combinatorial principles that hold in the constructible universe and that can be appended to any model of set theory by straightforward forcing. This principle has found wide application not only in the continuing investigation of set theory itself, but also to problems in more general mathematics that implicitly involve the transfinite. In the chapter, Wk is established as an independent and useful principle of construction. The chapter presents results to show the way by which these principles form a hierarchy of implications emanating only from the relatively simple proposition Wk. The chapter also discusses a form of Wk available at limit cardinals. Its relative consistency is established through a forcing technique involving a new kind of density argument. The chapter also discusses a Martin's Axiom-type characterization of morasses.

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