论文标题
$ \ mathbb Q $子环的波兰模块
Polish modules over subrings of $\mathbb Q$
论文作者
论文摘要
我们提供了一种通过$ \ Mathbb n $的子集的理想和$ \ Mathbb n $的序列的理想，从$ \ mathbb q $的任意子集中生产波兰模块的方法。该方法允许我们构建两个波兰$ \ Mathbb Q $ - 向量空间，$ u $和$ v $，以便 - $ u $和$ v $都嵌入$ \ mathbb r $，但 - $ u $不嵌入$ v $，$ v $不嵌入$ u $， 通过嵌入，我们了解连续的$ \ Mathbb Q $ - 线性注入。该结构回答了Frisch和Shinko的问题。实际上，我们的方法在嵌入式抛光$ \ mathbb q $ - 矢量空间方面产生了大量无与伦比。
We give a method of producing a Polish module over an arbitrary subring of $\mathbb Q$ from an ideal of subsets of $\mathbb N$ and a sequence in $\mathbb N$. The method allows us to construct two Polish $\mathbb Q$-vector spaces, $U$ and $V$, such that -- both $U$ and $V$ embed into $\mathbb R$ but -- $U$ does not embed into $V$ and $V$ does not embed into $U$, where by an embedding we understand a continuous $\mathbb Q$-linear injection. This construction answers a question of Frisch and Shinko. In fact, our method produces a large number of incomparable with respect to embeddings Polish $\mathbb Q$-vector spaces.
