کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778155 | 1633429 | 2017 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The â-variation of the Banach-Mazur game and forcing axioms
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We introduce a property of posets which strengthens (Ï1+1)-strategic closedness. This property is defined using a variation of the Banach-Mazur game on posets, where the first player chooses a countable set of conditions instead of a single condition at each turn. We prove PFA is preserved under any forcing over a poset with this property. As an application we reproduce a proof of Magidor's theorem about the consistency of PFA with some weak variations of the square principles. We also argue how different this property is from (Ï1+1)-operational closedness, which we introduced in our previous work, by observing which portions of MA+(Ï1-closed) are preserved or destroyed under forcing over posets with either property.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 6, June 2017, Pages 1335-1359
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 6, June 2017, Pages 1335-1359
نویسندگان
Yasuo Yoshinobu,