کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4662534 1633552 2006 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
More on the revised GCH and the black box
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
More on the revised GCH and the black box
چکیده انگلیسی

We strengthen the revised GCH theorem by showing, e.g., that for , for all but finitely many regular κ<ℶω, it holds that “λ is accessible on cofinality κ” in some weak sense (see below).As a corollary, λ=2μ=μ+>ℶω implies that the diamond holds on λ when restricted to cofinality κ for all but finitely many .We strengthen previous results on the black box and the middle diamond: previously it was established that these principles hold on for sufficiently large n; here we succeed in replacing a sufficiently large ℶn with a sufficiently large ℵn.The main theorem, concerning the accessibility of λ on cofinality κ, Theorem 3.1, implies as a special case that for every regular λ>ℶω, for some κ<ℶω, we can find a sequence 〈Pδ:δ<λ〉 such that , |Pδ|<λ, and we can fix a finite set d of “exceptional” regular cardinals θ<ℶω so that if A⊆λ satisfies |A|<ℶω, there is a pair-coloring so that for every -monochromatic B⊆A with no last element, letting δ:=supB it holds that B∈Pδ—provided that is not one of the finitely many “exceptional” members of d.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 140, Issues 1–3, July 2006, Pages 133-160