کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4661726 1633458 2014 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A model of Cummings and Foreman revisited
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
A model of Cummings and Foreman revisited
چکیده انگلیسی
This paper concerns the model of Cummings and Foreman where from ω supercompact cardinals they obtain the tree property at each ℵn for 2≤n<ω. We prove some structural facts about this model. We show that the combinatorics at ℵω+1 in this model depend strongly on the properties of ω1 in the ground model. From different ground models for the Cummings-Foreman iteration we can obtain either ℵω+1∈I[ℵω+1] and every stationary subset of ℵω+1 reflects or there are a bad scale at ℵω and a non-reflecting stationary subset of ℵω+1∩cof(ω1). We also prove that regardless of the ground model a strong generalization of the tree property holds at each ℵn for n≥2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 165, Issue 12, December 2014, Pages 1813-1831
نویسندگان
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