Year: 2014
Type: preprint
Abstract: This short note, prepared for the Logic Colloquium 2014, provides an introduction to Davies-trees and presents new applications in infinite combinatorics. In particular, we give new and simple proofs to the following theorems of P. Komjáth: every $n$-almost disjoint family of sets is essentially disjoint for any $n\in \mathbb N$; $\mathbb R^2$ is the union of $n+2$ clouds if the continuum is at most $\aleph_n$ for any $n\in \mathbb N$; every uncountably chromatic graph contains $n$-connected uncountably chromatic subgraphs for every $n\in \mathbb N$.
Source: arXiv (Cornell University)
Author: Soukup, Daniel T.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1434016993