Vol. 89, No. 1, 1980

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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
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
Authors
Jean Ann Larson
Richard Joseph Laver
George Frank McNulty