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
کلمات کلیدی
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
نویسندگان
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