论文标题
关于ZF中紧凑的Metrizable空间的几个惊人发现
Several amazing discoveries about compact metrizable spaces in ZF
论文作者
论文摘要
在没有选择的公理的情况下，研究了许多关于可迁移的紧凑型空间的自然陈述的固定理论状态。其中一些语句可证明在$ \ mathbf {zf} $中，有些说明与$ \ mathbf {zf} $无关。对于独立结果，应用了$ \ Mathbf {Zf} $的不同模型和$ \ Mathbf {Zfa} $的置换模型，并应用了Pincus的传输定理。构建了新的对称模型，在每种模型中，$ \ mathbb {r} $的功率集都是可以很好地订购的，连续假设是满足的，但是一个非空的有限套件的家族可以具有选择功能，并且不需要嵌入到Tychonoff Cube Cube Cube Cube $ [0，1] $ [0，1]^bevemblable striptum模型。
In the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $\mathbf{ZF}$, some are shown to be independent of $\mathbf{ZF}$. For independence results, distinct models of $\mathbf{ZF}$ and permutation models of $\mathbf{ZFA}$ with transfer theorems of Pincus are applied. New symmetric models are constructed in each of which the power set of $\mathbb{R}$ is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $[0, 1]^{\mathbb{R}}$.
