In the "Recursion Theory" book by C.T Chong, Liang Yu, towards the end of the book they list a few "open" research areas connected to higher computability theory. One such particular question is the following:

"Question A.3.2. Can one extend higher randomness theory to the entire analytical hierarchy under certain large cardinal assumptions?"

What I am intersted in is whether or not is anyone aware of this kind of research that was pursued after the publishing of this book, in this direction?



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