Preservation theorems for countable support forcing iterations

نویسنده

  • Chaz Schlindwein
چکیده

A major theme of [12] is preservation theorems for iterated forcing. These are theorems of the form “if 〈Pξ : ξ ≤ κ〉 is a countable support forcing iteration based on 〈Q̇ξ : ξ < κ〉 and each Q̇ξ has property such-and-such then Pκ has property thus-and-so.” The archetypal preservation theorem is the Fundamental Theorem of Proper Forcing [12, chapter III], which states that if each Q̇ξ is proper in V [GPξ ] then Pκ is proper. Typically, the property enjoyed by Pκ ensures that either ω1 is not collapsed, or that no new reals are added. In this paper we introduce two preservation theorems, one for not collapsing ω1 and one for not adding reals, which include many of the

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تاریخ انتشار 2008