Erdős-Rado theorem

Repeated exponentiationPlanetmathPlanetmath for cardinals is denoted expi(κ), where i<ω. It is defined by:




The Erdős-Rado theorem states that:


That is, if f:[expi(κ)+]i+1κ then there is a homogeneous set of size κ+.

As special cases, (2κ)+(κ+)κ2 and (20)+(1)02.

Title Erdős-Rado theorem
Canonical name ErdHosRadoTheorem
Date of creation 2013-03-22 12:59:30
Last modified on 2013-03-22 12:59:30
Owner Henry (455)
Last modified by Henry (455)
Numerical id 9
Author Henry (455)
Entry type Theorem
Classification msc 05D10
Classification msc 03E05
Related topic arrowsrelation
Related topic ArrowsRelation