关于大小为 $\aleph_0$ 的强稠密偏序集分裂性质的注记
组合数学
2026-01-14 v1 逻辑
摘要
我们证明了并非每个可数无穷强稠密偏序集都具有分裂性质，从而回答了 R. Ahlswede、P.L. Erdős 和 N. Graham 提出的一个问题。
引用
@article{arxiv.2601.08542,
title = {Note on the Splitting Property in Strongly Dense Posets of Size $\aleph_0$},
author = {Mirna Džamonja},
journal= {arXiv preprint arXiv:2601.08542},
year = {2026}
}
备注
This is an 1998 paper in where we have for the first time used the concept which is called "well-levelled'' orders in our recent preprint arXiv:2512.23003. In the 1998 paper we only used the second level of the well-levelled hierarchy, which is to take a tree and replace every one of its elements by a copy of the original tree. This process is called $T\cdot T$ in arXiv:2512.23003