Chaitin's work is genius, but one thing bugs me: he uses a Cantor space in exchange for Gödel's countable numbering. I haven't found any commentary on that, but

Chaitin's work is genius, but one thing bugs me: he uses a Cantor space in exchange for Gödel's countable numbering. I haven't found any commentary on that, but I find it suspicious. The problem with Cantor space is you simply can't even begin to approximate Chaitin's constant, but it seems like you could by using a countable numbering (all else being equal.) Of course that would blow everything up, so the takeaway is there is something very important which I'm not convinced we've learned yet.