论文标题
反向数学中的Brouwer不变性定理
The Brouwer invariance theorems in reverse mathematics
论文作者
论文摘要
约翰·斯蒂尔威尔（John Stillwell）在他的书中写道：“在我看来，找到布鲁维尔不变定理的确切优势似乎是反向数学中最有趣的开放问题之一。”在本文中，我们通过表明（某些形式的）Brouwer不变性定理解决了Stillwell的问题，相当于弱König的引理比基本系统$ {\ sf rca} _0 $。特别是，存在一种显式算法，每当弱könig的引理是错误的时，都会构建$ \ mathbb {r}^4 $的拓扑嵌入到$ \ mathbb {r}^3 $中。
In his book, John Stillwell wrote "finding the exact strength of the Brouwer invariance theorems seems to me one of the most interesting open problems in reverse mathematics." In this article, we solve Stillwell's problem by showing that (some forms of) the Brouwer invariance theorems are equivalent to weak König's lemma over the base system ${\sf RCA}_0$. In particular, there exists an explicit algorithm which, whenever weak König's lemma is false, constructs a topological embedding of $\mathbb{R}^4$ into $\mathbb{R}^3$.
