Dilworth's Theorem for Borel Posets
Combinatorics
2020-04-07 v1
Abstract
A famous theorem of Dilworth asserts that any finite poset of width can be decomposed into chains. We study the following problem: given a Borel poset of finite width , is it true that it can be decomposed into 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.
Cite
@article{arxiv.2004.02162,
title = {Dilworth's Theorem for Borel Posets},
author = {Bartłomiej Bosek and Jarosław Grytczuk and Zbigniew Lonc},
journal= {arXiv preprint arXiv:2004.02162},
year = {2020}
}