Universal graphs at ℵ_ω1+1

2016/05/02 by Jacob Davis, Davis, Jacob
Mathematics · Computer Science · #Advanced Topology and Set Theory #Advanced Graph Theory Research #Computability, Logic, AI Algorithms

paper · doi:10.48550/arxiv.1605.00605

Abstract

Starting from a supercompact cardinal we build a model in which 2^ℵ_ω1=2^ℵ_ω1+1=ℵ_ω1+3 but there is a jointly universal family of size ℵ_ω1+2 of graphs on ℵ_ω1+1. The same technique will work for any uncountable cardinal in place of ω₁.

Related

• Universal graphs at the successor of a singular cardinal
• Small universal families of graphs on ℵ_ω+1
• No universal graphs at uncountable regular cardinals
• Universal Graphs at ℵ_ω1+1 and Set-theoretic Geology
• Universal graphs between a strong limit singular and its power