Square-free and cube-free colorings of the ordinals

Jean Ann Larson, Richard Joseph Laver and George Frank McNulty

Vol. 89 (1980), No. 1, 137–141

DOI: 10.2140/pjm.1980.89.137

Abstract

We prove: Theorem 1. The class of all ordinals has a square-free 3-coloring and a cube-free 2-coloring. Theorem  2 Every k-th power-free n-coloring of α can be extended to a maximal k-th power-free n-coloring of β, for some β × α ⋅ ω, where k,n ∈ ω.

Mathematical Subject Classification 2000

Primary: 03E10

Secondary: 04A10

Milestones

Received: 7 February 1978

Published: 1 July 1980