A Turing Incomputable Coloring Function

Michael Stephen Fiske

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arXiv · 2312.02412

A Turing Incomputable Coloring Function

Michael Stephen Fiske

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Abstract

This paper describes a sequence of natural numbers that grows faster than any Turing computable function. This sequence is generated from a version of the tiling problem, called a coloring system. In our proof that generates the sequence, we use the notions of a chain and an unbounded sequence property, which resemble the methods of point set topology. From this sequence, we define a Turing incomputable coloring function.

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BibTeX RIS

Michael Stephen Fiske. 2023-12-05. A Turing Incomputable Coloring Function. https://arxiv.org/abs/2312.02412

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