Countably Complementable Linear Orderings
Countably Complementable Linear Orderings
复制标题
可数互补线性排序
DOI：
10.1007/s11083-006-9049-6
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发表时间：
2007
期刊：
影响因子：
0.4
通讯作者：
Antonio Montalbán
中科院分区：
文献类型：
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作者：
Antonio Montalbán
我们说一个可数线性序L$是可数可补的，如果存在一个可能不可数的线性序{L}$，使得对任何可数线性序B$，L都不嵌入到B中当且仅当B$嵌入到L中.我们刻画了可数可补的线性序。我们还证明了该性质等价于Hagendorf引入的有限忠实扩张性质的可数形式。利用类似的方法，引入弱可数可补线性序的概念，回答了Rosenstein提出的一个问题，证明了Hagdorf猜想的一个可数情形，即每个可数线性序满足完全忠实扩张性质的可数形式.
We say that a countable linear ordering $\mathcal L$ is countably complementable if there exists a linear ordering $\overline{\mathcal L}$, possibly uncountable, such that for any countable linear ordering $\mathcal B$,$\mathcal L$ does not embed into $\mathcal B$ if and only if $\mathcal B$ embeds into $\overline{\mathcal L}$. We characterize the linear orderings which are countably complementable. We also show that this property is equivalent to the countable version of the finitely faithful extension property introduced by Hagendorf. Using similar methods and introducing the notion of weakly countably complementable linear orderings, we answer a question posed by Rosenstein and prove the countable case of a conjecture of Hagendorf, namely, that every countable linear ordering satisfies the countable version of the totally faithful extension property.