添加超实数而不加实数的力迫（英文）

发布时间：2018-02-01 02:25

本文关键词： ω_-超实数 Mathias力迫支配性实数无界实数基数不变量　出处：《数学杂志》2017年05期 　论文类型：期刊论文

【摘要】：本文研究了加强型Mathias力迫及其在不可数情形下的推广.通过力迫法,证明了Mathias力迫添加支配性实数,而加强型Mathias力迫添加的是无界、非支配性的实数.还证明了ω_1上的Mathias型力迫添加的是无界、非支配性的ω_1类实数且不添加新的实数.这些结论可应用于对实数上的基数不变量的研究.
[Abstract]:In this paper, we study the augmented Mathias force and its extension in the case of uncountable conditions. By force forcing method, we prove that the Mathias force is forced to add the dominating real number. It is also proved that the forced addition of the Mathias type force on 蠅 _ s _ 1 is unbounded. The nondominant 蠅-class 1 real numbers without adding new real numbers. These conclusions can be applied to the study of cardinal invariants on real numbers.
【作者单位】：华南理工大学广州学院;
【基金】：Supported by National Natural Science Foundation of China(11401567)
【分类号】：O174.1
【正文快照】： 1 IntroductionForcing is a mechanism of obtaining independent results over the commonly acceptedfoundation of mathematics,the Zermelo-Fraenkel axiom system with the axiom of choice.Since its formulation by Cohen[1],forcing has become a powerful tool in a

【相似文献】