论文标题
Dilworth的Borel Posets定理
Dilworth's Theorem for Borel Posets
论文作者
论文摘要
著名的迪尔沃思（Dilworth）定理断言，任何有限的宽度$ k $的有限孔都可以分解为$ k $链。我们研究以下问题：鉴于有限宽度$ k $的Borel Poset $ p $，是否可以将其分解为$ k $ borel链？我们在可嵌入真实行的Borel Posets的特殊情况下给出了积极的答案。我们还证明了对POSET的双重定理，其可比性图在局部可数。
A famous theorem of Dilworth asserts that any finite poset of width $k$ can be decomposed into $k$ chains. We study the following problem: given a Borel poset $P$ of finite width $k$, is it true that it can be decomposed into $k$ Borel chains? We give a positive answer in a special case of Borel posets embeddable into the real line. We also prove a dual theorem for posets whose comparability graphs are locally countable.
