Section 48.6 Reflection
My assumption while tinkering with \(F_E\) is that it is not \(2\)–accessible, primarily by the computer evidence in [48.7.2]. However, Theorem 48.5.1 and Theorem 48.5.4 show how easy (relatively speaking) it is for a set to be accessible, which makes me suspect the possibility that the computer evidence is a symptom of the law of small numbers. I have entertaining the idea that \(F_E\) is not \(2\)–accessible for more time then it being \(2\)–accessible. So I am again uncertain whether or not \(F_E\) is \(2\)–accessible. If I return to this problem in the summer I will spend more time approach it from the prospective that it is \(2\)–accessible, and perhaps spending more time on this angle will aid in a colouring which avoids arbitrarily long monochromatic \(F_E\)–diffsequences.