کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904279 | 1633415 | 2018 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Characterizations of pretameness and the Ord-cc
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
It is well known that pretameness implies the forcing theorem, and that pretameness is characterized by the preservation of the axioms of ZFâ, that is ZF without the power set axiom, or equivalently, by the preservation of the axiom scheme of replacement, for class forcing over models of ZF. We show that pretameness in fact has various other characterizations, for instance in terms of the forcing theorem, the preservation of the axiom scheme of separation, the forcing equivalence of partial orders and their dense suborders, and the existence of nice names for sets of ordinals. These results show that pretameness is a strong dividing line between well and badly behaved notions of class forcing, and that it is exactly the right notion to consider in applications of class forcing. Furthermore, for most properties under consideration, we also present a corresponding characterization of the Ord-chain condition.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 169, Issue 8, August 2018, Pages 775-802
Journal: Annals of Pure and Applied Logic - Volume 169, Issue 8, August 2018, Pages 775-802
نویسندگان
Peter Holy, Regula Krapf, Philipp Schlicht,