کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778135 | 1633430 | 2017 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Characterizing large cardinals in terms of layered posets
ترجمه فارسی عنوان
مشخص کردن کاردینال های بزرگ از لحاظ لایه های لایه ای
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
چکیده انگلیسی
Given an uncountable regular cardinal κ, a partial order is κ-stationarily layered if the collection of regular suborders of P of cardinality less than κ is stationary in Pκ(P). We show that weak compactness can be characterized by this property of partial orders by proving that an uncountable regular cardinal κ is weakly compact if and only if every partial order satisfying the κ-chain condition is κ-stationarily layered. We prove a similar result for strongly inaccessible cardinals. Moreover, we show that the statement that all κ-Knaster partial orders are κ-stationarily layered implies that κ is a Mahlo cardinal and every stationary subset of κ reflects. This shows that this statement characterizes weak compactness in canonical inner models. In contrast, we show that it is also consistent that this statement holds at a non-weakly compact cardinal.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 5, May 2017, Pages 1112-1131
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 5, May 2017, Pages 1112-1131
نویسندگان
Sean Cox, Philipp Lücke,