科研之友
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摘要
We study the approachability ideal I[kappa(+)] in the context of large cardinals and properties of the regular cardinals below a singular kappa. As a guiding example consider the approachability ideal I[Nw+1] assuming that N-w, is a strong limit. In this case we obtain that club many points in Nw+1 of cofinality N-n for some n > 1 are approachable assuming the joint reflection of countable families of stationary subsets of N-n. This reflection principle holds under MM for all n > 1 and for each n > 1 is equiconsistent with N-n being weakly compact in L. This characterizes the structure of the approachability ideal I[Nw+1] in models of MM. We also apply our result to show that the Chang conjecture (kappa(+), kappa)-> (N-2, N-1) fails in models of MM for all singular cardinals kappa.
- 出版日期2010-8
