Bootstrapping the Primitive Recursive Functions by 47 Colors

Søren Riis


I construct a concrete coloring of the 3 element subsets of N. It has the property that each homogeneous set {s_0, s_1, s_2, ..., s_r}, r >= s_0 - 1 has its elements spread so much apart that F_{omega}(s_i) < s_{i+1} for i = 1, 2, ..., r -1. It uses only 47 colors. This is more economical than the approximately 160000 colors used by Ketonen and Solovay.

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ISSN: 0909-0878 

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