Coloring finite subsets of uncountable sets
Abstract
It is consistent for every (1 <= n< omega) that (2omega = omegan) and there is a function (F:[omegan]< omega-> omega) such that every finite set can be written at most (2n-1) ways as the union of two distinct monocolored sets. If GCH holds, for every such coloring there is a finite set that can be written at least (sumni=1n+i choose nn choose i) ways as the union of two sets with the same color.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.