The internal consistency of Easton's theorem
نویسندگان
چکیده
Let Card denote the class of infinite cardinals and Reg the class of infinite regular cardinals. The continuum function on regulars is the function κ 7→ 2, defined on Reg. This function C has the following two properties: α ≤ β → C(α) ≤ C(β) and α < cof (C(α)). Easton [2] showed that, assuming GCH, any function F : Reg → Card with these two properties (any “Easton function”) is the continuum function on regulars of a cofinalitypreserving generic extension of the universe. We say that this generic extension “realises” the Easton function F . In particular, the statement “2 = κ for all regular κ” is consistent, as by Easton’s result it can be forced over Gödel’s universe L.
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ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 156 شماره
صفحات -
تاریخ انتشار 2008